Solve for x 3(x+1)^2-15=-12

$3 {(x + 1)}^{2} - 15 = - 12$

Step 1

Add $15$ to both sides of the equation.

$3 {(x + 1)}^{2} = - 12 + 15$

Step 2

Add $- 12$ and $15$ .

$3 {(x + 1)}^{2} = 3$

Step 3

Divide each term in $3 {(x + 1)}^{2} = 3$ by $3$ and simplify.

Divide each term in $3 {(x + 1)}^{2} = 3$ by $3$ .

$\frac{3 {(x + 1)}^{2}}{3} = \frac{3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 {(x + 1)}^{2}}{3} = \frac{3}{3}$

Divide ${(x + 1)}^{2}$ by $1$ .

${(x + 1)}^{2} = \frac{3}{3}$

Simplify the right side.

Divide $3$ by $3$ .

${(x + 1)}^{2} = 1$

Step 4

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x + 1 = \pm \sqrt{1}$

Step 5

Any root of $1$ is $1$ .

$x + 1 = \pm 1$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x + 1 = 1$

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$x = 1 - 1$

Subtract $1$ from $1$ .

$x = 0$

Next, use the negative value of the $\pm$ to find the second solution.

$x + 1 = - 1$

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$x = - 1 - 1$

Subtract $1$ from $- 1$ .

$x = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 0, - 2$