(x+4)x(4)=128

Solution for (x+4)x(4)=128 equation:

Simplifying
(x + 4) * x(4) = 128

Reorder the terms:
(4 + x) * x(4) = 128

Reorder the terms for easier multiplication:
4x(4 + x) = 128
(4 * 4x + x * 4x) = 128
(16x + 4x2) = 128

Solving
16x + 4x2 = 128

Solving for variable 'x'.

Reorder the terms:
-128 + 16x + 4x2 = 128 + -128

Combine like terms: 128 + -128 = 0
-128 + 16x + 4x2 = 0

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

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-8, 4}