Question Solve for $d$ in the equation $(4d+5)(d+9)=0$ . Write the solutions as integers or simplified fractions.

Studdy Solution

STEP 1

1. The equation $(4d+5)(d+9)=0$ is a product of two linear factors set equal to zero.
2. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 2

1. Apply the Zero Product Property to find the values of $d$ that make each factor equal to zero.
2. Simplify the solutions to ensure they are in the simplest form.

STEP 3

Apply the Zero Product Property to set each factor equal to zero separately.
$4d + 5 = 0 \quad \text{or} \quad d + 9 = 0$

STEP 4

Solve the first equation for $d$ .
$4d + 5 = 0 \implies 4d = -5 \implies d = -\frac{5}{4}$

STEP 5

Solve the second equation for $d$ .
$d + 9 = 0 \implies d = -9$

STEP 6

Ensure that the solutions are in the simplest form.
The solutions $d = -\frac{5}{4}$ and $d = -9$ are already in their simplest form as integers or fractions.
The solutions to the equation $(4d+5)(d+9)=0$ are: $d = -\frac{5}{4}$ $\text{or} \quad d = -9$

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Question Solve for $d$ in the equation $(4d+5)(d+9)=0$ . Write the solutions as integers or simplified fractions.

Studdy Solution

STEP 1

1. The equation $(4d+5)(d+9)=0$ is a product of two linear factors set equal to zero.
2. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 2

1. Apply the Zero Product Property to find the values of $d$ that make each factor equal to zero.
2. Simplify the solutions to ensure they are in the simplest form.

STEP 3

Apply the Zero Product Property to set each factor equal to zero separately.
$4d + 5 = 0 \quad \text{or} \quad d + 9 = 0$

STEP 4

Solve the first equation for $d$ .
$4d + 5 = 0 \implies 4d = -5 \implies d = -\frac{5}{4}$

STEP 5

Solve the second equation for $d$ .
$d + 9 = 0 \implies d = -9$

STEP 6

Ensure that the solutions are in the simplest form.
The solutions $d = -\frac{5}{4}$ and $d = -9$ are already in their simplest form as integers or fractions.
The solutions to the equation $(4d+5)(d+9)=0$ are: $d = -\frac{5}{4}$ $\text{or} \quad d = -9$

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Question Solve for ddd in the equation (4d+5)(d+9)=0(4d+5)(d+9)=0(4d+5)(d+9)=0. Write the solutions as integers or simplified fractions.

Studdy Solution

STEP 1

1. The equation (4d+5)(d+9)=0(4d+5)(d+9)=0(4d+5)(d+9)=0 is a product of two linear factors set equal to zero.2. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 2

1. Apply the Zero Product Property to find the values of ddd that make each factor equal to zero.2. Simplify the solutions to ensure they are in the simplest form.

STEP 3

Apply the Zero Product Property to set each factor equal to zero separately.4d+5=0ord+9=0 4d + 5 = 0 \quad \text{or} \quad d + 9 = 0 4d+5=0ord+9=0

STEP 4

Solve the first equation for ddd.4d+5=0 ⟹ 4d=−5 ⟹ d=−54 4d + 5 = 0 \implies 4d = -5 \implies d = -\frac{5}{4} 4d+5=0⟹4d=−5⟹d=−45​

STEP 5

Solve the second equation for ddd.d+9=0 ⟹ d=−9 d + 9 = 0 \implies d = -9 d+9=0⟹d=−9

STEP 6

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Question Solve for $d$ in the equation $(4d+5)(d+9)=0$ . Write the solutions as integers or simplified fractions.

1. The equation $(4d+5)(d+9)=0$ is a product of two linear factors set equal to zero.
2. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

1. Apply the Zero Product Property to find the values of $d$ that make each factor equal to zero.
2. Simplify the solutions to ensure they are in the simplest form.

Apply the Zero Product Property to set each factor equal to zero separately.
$4d + 5 = 0 \quad \text{or} \quad d + 9 = 0$

Solve the first equation for $d$ .
$4d + 5 = 0 \implies 4d = -5 \implies d = -\frac{5}{4}$

Solve the second equation for $d$ .
$d + 9 = 0 \implies d = -9$