Solve for z (6z+6)^2=0

${(6 z + 6)}^{2} = 0$

Factor the left side of the equation.

Factor $6$ out of $6 z + 6$ .

Factor $6$ out of $6 z$ .

${(6 (z) + 6)}^{2} = 0$

Factor $6$ out of $6$ .

${(6 (z) + 6 (1))}^{2} = 0$

Factor $6$ out of $6 (z) + 6 (1)$ .

${(6 (z + 1))}^{2} = 0$

Apply the product rule to $6 (z + 1)$ .

$6^{2} {(z + 1)}^{2} = 0$

Divide each term in $6^{2} {(z + 1)}^{2} = 0$ by $6^{2}$ and simplify.

Divide each term in $6^{2} {(z + 1)}^{2} = 0$ by $6^{2}$ .

$\frac{6^{2} {(z + 1)}^{2}}{6^{2}} = \frac{0}{6^{2}}$

Simplify the left side.

Cancel the common factor of $6^{2}$ .

Cancel the common factor.

$\frac{6^{2} {(z + 1)}^{2}}{6^{2}} = \frac{0}{6^{2}}$

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

${(z + 1)}^{2} = \frac{0}{6^{2}}$

Simplify the right side.

Raise $6$ to the power of $2$ .

${(z + 1)}^{2} = \frac{0}{36}$

Divide $0$ by $36$ .

${(z + 1)}^{2} = 0$

Set the $z + 1$ equal to $0$ .

$z + 1 = 0$

Subtract $1$ from both sides of the equation.

$z = - 1$