120=72+60x-12x^2

Solution for 120=72+60x-12x^2 equation:

Simplifying
120 = 72 + 60x + -12x2

Solving
120 = 72 + 60x + -12x2

Solving for variable 'x'.

Combine like terms: 120 + -72 = 48
48 + -60x + 12x2 = 72 + 60x + -12x2 + -72 + -60x + 12x2

Reorder the terms:
48 + -60x + 12x2 = 72 + -72 + 60x + -60x + -12x2 + 12x2

Combine like terms: 72 + -72 = 0
48 + -60x + 12x2 = 0 + 60x + -60x + -12x2 + 12x2
48 + -60x + 12x2 = 60x + -60x + -12x2 + 12x2

Combine like terms: 60x + -60x = 0
48 + -60x + 12x2 = 0 + -12x2 + 12x2
48 + -60x + 12x2 = -12x2 + 12x2

Combine like terms: -12x2 + 12x2 = 0
48 + -60x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(4 + -5x + x2) = 0

Factor a trinomial.
12((1 + -1x)(4 + -1x)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
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 = {1, 4}