4x^2+120x=256

Solution for 4x^2+120x=256 equation:

Simplifying
4x2 + 120x = 256

Reorder the terms:
120x + 4x2 = 256

Solving
120x + 4x2 = 256

Solving for variable 'x'.

Reorder the terms:
-256 + 120x + 4x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + 120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-64 + 30x + x2) = 0

Factor a trinomial.
4((-32 + -1x)(2 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-32 + -1x)' equal to zero and attempt to solve:

Simplifying
-32 + -1x = 0

Solving
-32 + -1x = 0

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

Add '32' to each side of the equation.
-32 + 32 + -1x = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1x = 0 + 32
-1x = 0 + 32

Combine like terms: 0 + 32 = 32
-1x = 32

Divide each side by '-1'.
x = -32

Simplifying
x = -32
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 = {-32, 2}