Find the Roots (Zeros) (x+7)^3(x-2i)(x+2i)=0

${(x + 7)}^{3} (x - 2 i) (x + 2 i) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

${(x + 7)}^{3} = 0$

$x - 2 i = 0$

$x + 2 i = 0$

Set ${(x + 7)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(x + 7)}^{3}$ equal to $0$ .

${(x + 7)}^{3} = 0$

Solve ${(x + 7)}^{3} = 0$ for $x$ .

Set the $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

Set $x - 2 i$ equal to $0$ and solve for $x$ .

Set $x - 2 i$ equal to $0$ .

$x - 2 i = 0$

Add $2 i$ to both sides of the equation.

$x = 2 i$

Set $x + 2 i$ equal to $0$ and solve for $x$ .

Set $x + 2 i$ equal to $0$ .

$x + 2 i = 0$

Subtract $2 i$ from both sides of the equation.

$x = - 2 i$

The final solution is all the values that make ${(x + 7)}^{3} (x - 2 i) (x + 2 i) = 0$ true.

$x = - 7, 2 i, - 2 i$