x^2(8x-3)4(8x+3)=0

Solution for x^2(8x-3)4(8x+3)=0 equation:

Simplifying
x2(8x + -3) * 4(8x + 3) = 0

Reorder the terms:
x2(-3 + 8x) * 4(8x + 3) = 0

Reorder the terms:
x2(-3 + 8x) * 4(3 + 8x) = 0

Reorder the terms for easier multiplication:
4x2(-3 + 8x)(3 + 8x) = 0

Multiply (-3 + 8x) * (3 + 8x)
4x2(-3(3 + 8x) + 8x * (3 + 8x)) = 0
4x2((3 * -3 + 8x * -3) + 8x * (3 + 8x)) = 0
4x2((-9 + -24x) + 8x * (3 + 8x)) = 0
4x2(-9 + -24x + (3 * 8x + 8x * 8x)) = 0
4x2(-9 + -24x + (24x + 64x2)) = 0

Combine like terms: -24x + 24x = 0
4x2(-9 + 0 + 64x2) = 0
4x2(-9 + 64x2) = 0
(-9 * 4x2 + 64x2 * 4x2) = 0
(-36x2 + 256x4) = 0

Solving
-36x2 + 256x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-9 + 64x2) = 0

Factor a difference between two squares.
4x2((3 + 8x)(-3 + 8x)) = 0

Ignore the factor 4.
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 '(3 + 8x)' equal to zero and attempt to solve:

Simplifying
3 + 8x = 0

Solving
3 + 8x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8x = 0 + -3
8x = 0 + -3

Combine like terms: 0 + -3 = -3
8x = -3

Divide each side by '8'.
x = -0.375

Simplifying
x = -0.375
Subproblem 3
Set the factor '(-3 + 8x)' equal to zero and attempt to solve:

Simplifying
-3 + 8x = 0

Solving
-3 + 8x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 8x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 8x = 0 + 3
8x = 0 + 3

Combine like terms: 0 + 3 = 3
8x = 3

Divide each side by '8'.
x = 0.375

Simplifying
x = 0.375
Solution
x = {0, -0.375, 0.375}