x(120-2x)=1512

Solution for x(120-2x)=1512 equation:

Simplifying
x(120 + -2x) = 1512
(120 * x + -2x * x) = 1512
(120x + -2x2) = 1512

Solving
120x + -2x2 = 1512

Solving for variable 'x'.

Reorder the terms:
-1512 + 120x + -2x2 = 1512 + -1512

Combine like terms: 1512 + -1512 = 0
-1512 + 120x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-756 + 60x + -1x2) = 0

Factor a trinomial.
2((-42 + x)(18 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-42 + x)' equal to zero and attempt to solve:

Simplifying
-42 + x = 0

Solving
-42 + x = 0

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

Add '42' to each side of the equation.
-42 + 42 + x = 0 + 42

Combine like terms: -42 + 42 = 0
0 + x = 0 + 42
x = 0 + 42

Combine like terms: 0 + 42 = 42
x = 42

Simplifying
x = 42
Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {42, 18}