x^2(8x+9)(8x-9)=0

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

Simplifying
x2(8x + 9)(8x + -9) = 0

Reorder the terms:
x2(9 + 8x)(8x + -9) = 0

Reorder the terms:
x2(9 + 8x)(-9 + 8x) = 0

Multiply (9 + 8x) * (-9 + 8x)
x2(9(-9 + 8x) + 8x * (-9 + 8x)) = 0
x2((-9 * 9 + 8x * 9) + 8x * (-9 + 8x)) = 0
x2((-81 + 72x) + 8x * (-9 + 8x)) = 0
x2(-81 + 72x + (-9 * 8x + 8x * 8x)) = 0
x2(-81 + 72x + (-72x + 64x2)) = 0

Combine like terms: 72x + -72x = 0
x2(-81 + 0 + 64x2) = 0
x2(-81 + 64x2) = 0
(-81 * x2 + 64x2 * x2) = 0
(-81x2 + 64x4) = 0

Solving
-81x2 + 64x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-81 + 64x2) = 0

Factor a difference between two squares.
x2((9 + 8x)(-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
Subproblem 3
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, 1.125}