2x^2-64=8x

Solution for 2x^2-64=8x equation:

Simplifying
2x2 + -64 = 8x

Reorder the terms:
-64 + 2x2 = 8x

Solving
-64 + 2x2 = 8x

Solving for variable 'x'.

Reorder the terms:
-64 + -8x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-64 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + -4x + x2) = 0

Factor a trinomial.
2((-4 + -1x)(8 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-4, 8}