Question Find solutions to the quadratic equation $2n(3n-12)=0$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $2n(3n - 12) = 0$ .
2. We need to find the values of $n$ that satisfy this equation.

STEP 2

To solve the equation, we will use the zero product property, which states that if the product of two numbers is zero, then at least one of the factors must be zero.
$2n(3n - 12) = 0$

STEP 3

Set each factor equal to zero and solve for $n$ .
First factor: $2n = 0$
Second factor: $(3n - 12) = 0$

STEP 4

Solve the first equation for $n$ .
$2n = 0$
Divide both sides by 2:
$\frac{2n}{2} = \frac{0}{2}$

STEP 5

Calculate the value of $n$ from the first equation.
$n = 0$

STEP 6

Solve the second equation for $n$ .
$3n - 12 = 0$
Add 12 to both sides:
$3n = 12$

STEP 7

Divide both sides by 3 to find the value of $n$ .
$\frac{3n}{3} = \frac{12}{3}$

STEP 8

Calculate the value of $n$ from the second equation.
$n = 4$

STEP 9

List the solutions for $n$ from both equations.
The solutions are $n = 0$ and $n = 4$ .
Therefore, the correct answer is A. 0 and 4.

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Question Find solutions to the quadratic equation $2n(3n-12)=0$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $2n(3n - 12) = 0$ .
2. We need to find the values of $n$ that satisfy this equation.

STEP 2

To solve the equation, we will use the zero product property, which states that if the product of two numbers is zero, then at least one of the factors must be zero.
$2n(3n - 12) = 0$

STEP 3

Set each factor equal to zero and solve for $n$ .
First factor: $2n = 0$
Second factor: $(3n - 12) = 0$

STEP 4

Solve the first equation for $n$ .
$2n = 0$
Divide both sides by 2:
$\frac{2n}{2} = \frac{0}{2}$

STEP 5

Calculate the value of $n$ from the first equation.
$n = 0$

STEP 6

Solve the second equation for $n$ .
$3n - 12 = 0$
Add 12 to both sides:
$3n = 12$

STEP 7

Divide both sides by 3 to find the value of $n$ .
$\frac{3n}{3} = \frac{12}{3}$

STEP 8

Calculate the value of $n$ from the second equation.
$n = 4$

STEP 9

List the solutions for $n$ from both equations.
The solutions are $n = 0$ and $n = 4$ .
Therefore, the correct answer is A. 0 and 4.

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Question Find solutions to the quadratic equation 2n(3n−12)=02n(3n-12)=02n(3n−12)=0.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 2n(3n−12)=02n(3n - 12) = 02n(3n−12)=0.2. We need to find the values of nnn that satisfy this equation.

STEP 2

To solve the equation, we will use the zero product property, which states that if the product of two numbers is zero, then at least one of the factors must be zero.2n(3n−12)=02n(3n - 12) = 02n(3n−12)=0

STEP 3

Set each factor equal to zero and solve for nnn.First factor: 2n=02n = 02n=0Second factor: (3n−12)=0(3n - 12) = 0(3n−12)=0

STEP 4

Solve the first equation for nnn.2n=02n = 02n=0Divide both sides by 2:2n2=02\frac{2n}{2} = \frac{0}{2}22n​=20​

STEP 5

Calculate the value of nnn from the first equation.n=0n = 0n=0

STEP 6

Solve the second equation for nnn.3n−12=03n - 12 = 03n−12=0Add 12 to both sides:3n=123n = 123n=12

STEP 7

Divide both sides by 3 to find the value of nnn.3n3=123\frac{3n}{3} = \frac{12}{3}33n​=312​

STEP 8

Calculate the value of nnn from the second equation.n=4n = 4n=4

STEP 9

List the solutions for nnn from both equations.The solutions are n=0n = 0n=0 and n=4n = 4n=4.Therefore, the correct answer is A. 0 and 4.

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Question Find solutions to the quadratic equation $2n(3n-12)=0$ .

Assumptions
1. We are given the equation $2n(3n - 12) = 0$ .
2. We need to find the values of $n$ that satisfy this equation.

To solve the equation, we will use the zero product property, which states that if the product of two numbers is zero, then at least one of the factors must be zero.
$2n(3n - 12) = 0$

Set each factor equal to zero and solve for $n$ .
First factor: $2n = 0$
Second factor: $(3n - 12) = 0$

Solve the first equation for $n$ .
$2n = 0$
Divide both sides by 2:
$\frac{2n}{2} = \frac{0}{2}$

Calculate the value of $n$ from the first equation.
$n = 0$

Solve the second equation for $n$ .
$3n - 12 = 0$
Add 12 to both sides:
$3n = 12$

Divide both sides by 3 to find the value of $n$ .
$\frac{3n}{3} = \frac{12}{3}$

Calculate the value of $n$ from the second equation.
$n = 4$

List the solutions for $n$ from both equations.
The solutions are $n = 0$ and $n = 4$ .
Therefore, the correct answer is A. 0 and 4.