x^2(9+8x)=0

Solution for x^2(9+8x)=0 equation:

Simplifying
x2(9 + 8x) = 0
(9 * x2 + 8x * x2) = 0
(9x2 + 8x3) = 0

Solving
9x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(9 + 8x) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(9 + 8x)' equal to zero and attempt to solve:

Simplifying
9 + 8x = 0

Solving
9 + 8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + 8x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8x = 0 + -9
8x = 0 + -9

Combine like terms: 0 + -9 = -9
8x = -9

Divide each side by '8'.
x = -1.125

Simplifying
x = -1.125
Solution
x = {0, -1.125}