Solve for x 3(x+1)^2=27

$3 {(x + 1)}^{2} = 27$

Divide each term in $3 {(x + 1)}^{2} = 27$ by $3$ and simplify.

Divide each term in $3 {(x + 1)}^{2} = 27$ by $3$ .

$\frac{3 {(x + 1)}^{2}}{3} = \frac{27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 {(x + 1)}^{2}}{3} = \frac{27}{3}$

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

${(x + 1)}^{2} = \frac{27}{3}$

Simplify the right side.

Divide $27$ by $3$ .

${(x + 1)}^{2} = 9$

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

$x + 1 = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x + 1 = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x + 1 = \pm 3$

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.

$x + 1 = 3$

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

Subtract $1$ from both sides of the equation.

$x = 3 - 1$

Subtract $1$ from $3$ .

$x = 2$

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

$x + 1 = - 3$

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

Subtract $1$ from both sides of the equation.

$x = - 3 - 1$

Subtract $1$ from $- 3$ .

$x = - 4$

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

$x = 2, - 4$