4x^2+4x=120

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

Simplifying
4x2 + 4x = 120

Reorder the terms:
4x + 4x2 = 120

Solving
4x + 4x2 = 120

Solving for variable 'x'.

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

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

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

Factor a trinomial.
4((-6 + -1x)(5 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}