120=4x(x+1)

Solution for 120=4x(x+1) equation:

Simplifying
120 = 4x(x + 1)

Reorder the terms:
120 = 4x(1 + x)
120 = (1 * 4x + x * 4x)
120 = (4x + 4x2)

Solving
120 = 4x + 4x2

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + -1x + -1x2) = 0

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

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