32x-32=8x^2

Solution for 32x-32=8x^2 equation:

Simplifying
32x + -32 = 8x2

Reorder the terms:
-32 + 32x = 8x2

Solving
-32 + 32x = 8x2

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + 4x + -1x2) = 0

Factor a trinomial.
8((-2 + x)(2 + -1x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {2, 2}