2x(2x-8)=-16

Solution for 2x(2x-8)=-16 equation:

Simplifying
2x(2x + -8) = -16

Reorder the terms:
2x(-8 + 2x) = -16
(-8 * 2x + 2x * 2x) = -16
(-16x + 4x2) = -16

Solving
-16x + 4x2 = -16

Solving for variable 'x'.

Reorder the terms:
16 + -16x + 4x2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + -16x + 4x2 = 0

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

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

Ignore the factor 4.
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}