x(2x+16)=256

Solution for x(2x+16)=256 equation:

Simplifying
x(2x + 16) = 256

Reorder the terms:
x(16 + 2x) = 256
(16 * x + 2x * x) = 256
(16x + 2x2) = 256

Solving
16x + 2x2 = 256

Solving for variable 'x'.

Reorder the terms:
-256 + 16x + 2x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-128 + 8x + x2) = 0

Factor a trinomial.
2((-16 + -1x)(8 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
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 = {-16, 8}