Solve for x (x+7)^3+8=16

${(x + 7)}^{3} + 8 = 16$

Subtract $8$ from both sides of the equation.

${(x + 7)}^{3} = 16 - 8$

Subtract $8$ from $16$ .

${(x + 7)}^{3} = 8$

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

$x + 7 = \sqrt[3]{8}$

Simplify $\sqrt[3]{8}$ .

Rewrite $8$ as $2^{3}$ .

$x + 7 = \sqrt[3]{2^{3}}$

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

$x + 7 = 2$

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

Subtract $7$ from both sides of the equation.

$x = 2 - 7$

Subtract $7$ from $2$ .

$x = - 5$