8x^2=8x+16

Solution for 8x^2=8x+16 equation:

Simplifying
8x2 = 8x + 16

Reorder the terms:
8x2 = 16 + 8x

Solving
8x2 = 16 + 8x

Solving for variable 'x'.

Reorder the terms:
-16 + -8x + 8x2 = 16 + 8x + -16 + -8x

Reorder the terms:
-16 + -8x + 8x2 = 16 + -16 + 8x + -8x

Combine like terms: 16 + -16 = 0
-16 + -8x + 8x2 = 0 + 8x + -8x
-16 + -8x + 8x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-16 + -8x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + -1x + x2) = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
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 = {-1, 2}