Solved on Feb 20, 2024

Solve for the value of $d$ that satisfies the equation $(d-7)(5d-2)=0$ .

STEP 1

Assumptions
1. We are given the equation $(d-7)(5d-2)=0$ .
2. We need to solve for the variable $d$ .
3. The solutions for $d$ should be written as integers or as proper or improper fractions.

STEP 2

To solve the equation $(d-7)(5d-2)=0$ , we will use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 3

Set each factor equal to zero and solve for $d$ .
For the first factor: $d-7=0$

STEP 4

Add 7 to both sides of the equation to solve for $d$ .
$d-7+7=0+7$

STEP 5

Simplify the equation to find the value of $d$ .
$d=7$

STEP 6

Now, set the second factor equal to zero and solve for $d$ .
For the second factor: $5d-2=0$

STEP 7

Add 2 to both sides of the equation to isolate the term with $d$ .
$5d-2+2=0+2$

STEP 8

Simplify the equation to find the value of $d$ .
$5d=2$

STEP 9

Divide both sides of the equation by 5 to solve for $d$ .
$\frac{5d}{5}=\frac{2}{5}$

STEP 10

Simplify the equation to find the value of $d$ .
$d=\frac{2}{5}$

STEP 11

Combine the solutions from STEP_5 and STEP_10.
The solutions for $d$ are: $d=7 \text{ or } d=\frac{2}{5}$

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Solve for the value of $d$ that satisfies the equation $(d-7)(5d-2)=0$ .

STEP 1

Assumptions
1. We are given the equation $(d-7)(5d-2)=0$ .
2. We need to solve for the variable $d$ .
3. The solutions for $d$ should be written as integers or as proper or improper fractions.

STEP 2

To solve the equation $(d-7)(5d-2)=0$ , we will use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 3

Set each factor equal to zero and solve for $d$ .
For the first factor: $d-7=0$

STEP 4

Add 7 to both sides of the equation to solve for $d$ .
$d-7+7=0+7$

STEP 5

Simplify the equation to find the value of $d$ .
$d=7$

STEP 6

Now, set the second factor equal to zero and solve for $d$ .
For the second factor: $5d-2=0$

STEP 7

Add 2 to both sides of the equation to isolate the term with $d$ .
$5d-2+2=0+2$

STEP 8

Simplify the equation to find the value of $d$ .
$5d=2$

STEP 9

Divide both sides of the equation by 5 to solve for $d$ .
$\frac{5d}{5}=\frac{2}{5}$

STEP 10

Simplify the equation to find the value of $d$ .
$d=\frac{2}{5}$

STEP 11

Combine the solutions from STEP_5 and STEP_10.
The solutions for $d$ are: $d=7 \text{ or } d=\frac{2}{5}$

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Solve for the value of ddd that satisfies the equation (d−7)(5d−2)=0(d-7)(5d-2)=0(d−7)(5d−2)=0.

STEP 1

Assumptions1. We are given the equation (d−7)(5d−2)=0(d-7)(5d-2)=0(d−7)(5d−2)=0.2. We need to solve for the variable ddd.3. The solutions for ddd should be written as integers or as proper or improper fractions.

STEP 2

To solve the equation (d−7)(5d−2)=0(d-7)(5d-2)=0(d−7)(5d−2)=0, we will use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 3

Set each factor equal to zero and solve for ddd.For the first factor: d−7=0d-7=0d−7=0

STEP 4

Add 7 to both sides of the equation to solve for ddd.d−7+7=0+7d-7+7=0+7d−7+7=0+7

STEP 5

Simplify the equation to find the value of ddd.d=7d=7d=7

STEP 6

Now, set the second factor equal to zero and solve for ddd.For the second factor: 5d−2=05d-2=05d−2=0

STEP 7

Add 2 to both sides of the equation to isolate the term with ddd.5d−2+2=0+25d-2+2=0+25d−2+2=0+2

STEP 8

Simplify the equation to find the value of ddd.5d=25d=25d=2

STEP 9

Divide both sides of the equation by 5 to solve for ddd.5d5=25\frac{5d}{5}=\frac{2}{5}55d​=52​

STEP 10

Simplify the equation to find the value of ddd.d=25d=\frac{2}{5}d=52​

STEP 11

Combine the solutions from STEP_5 and STEP_10.The solutions for ddd are: d=7 or d=25d=7 \text{ or } d=\frac{2}{5}d=7 or d=52​

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve for the value of $d$ that satisfies the equation $(d-7)(5d-2)=0$ .

Assumptions
1. We are given the equation $(d-7)(5d-2)=0$ .
2. We need to solve for the variable $d$ .
3. The solutions for $d$ should be written as integers or as proper or improper fractions.

To solve the equation $(d-7)(5d-2)=0$ , we will use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Set each factor equal to zero and solve for $d$ .
For the first factor: $d-7=0$

Add 7 to both sides of the equation to solve for $d$ .
$d-7+7=0+7$

Simplify the equation to find the value of $d$ .
$d=7$

Now, set the second factor equal to zero and solve for $d$ .
For the second factor: $5d-2=0$

Add 2 to both sides of the equation to isolate the term with $d$ .
$5d-2+2=0+2$

Simplify the equation to find the value of $d$ .
$5d=2$

Divide both sides of the equation by 5 to solve for $d$ .
$\frac{5d}{5}=\frac{2}{5}$

Simplify the equation to find the value of $d$ .
$d=\frac{2}{5}$

Combine the solutions from STEP_5 and STEP_10.
The solutions for $d$ are: $d=7 \text{ or } d=\frac{2}{5}$