8x(x-3)-32x^2=0

Solution for 8x(x-3)-32x^2=0 equation:

Simplifying
8x(x + -3) + -32x2 = 0

Reorder the terms:
8x(-3 + x) + -32x2 = 0
(-3 * 8x + x * 8x) + -32x2 = 0
(-24x + 8x2) + -32x2 = 0

Combine like terms: 8x2 + -32x2 = -24x2
-24x + -24x2 = 0

Solving
-24x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-24x'.
-24x(1 + x) = 0

Ignore the factor -24.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {0, -1}