(120-10x)(6+x)=0

Solution for (120-10x)(6+x)=0 equation:

Simplifying
(120 + -10x)(6 + x) = 0

Multiply (120 + -10x) * (6 + x)
(120(6 + x) + -10x * (6 + x)) = 0
((6 * 120 + x * 120) + -10x * (6 + x)) = 0
((720 + 120x) + -10x * (6 + x)) = 0
(720 + 120x + (6 * -10x + x * -10x)) = 0
(720 + 120x + (-60x + -10x2)) = 0

Combine like terms: 120x + -60x = 60x
(720 + 60x + -10x2) = 0

Solving
720 + 60x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(72 + 6x + -1x2) = 0

Factor a trinomial.
10((12 + -1x)(6 + x)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
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 = {12, -6}