8=-2x^2+8x

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

Simplifying
8 = -2x2 + 8x

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

Solving
8 = 8x + -2x2

Solving for variable 'x'.

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

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

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

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

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

Ignore the factor 2.
Subproblem 1
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
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}