(x-30)(x-120)=0

Solution for (x-30)(x-120)=0 equation:

Simplifying
(x + -30)(x + -120) = 0

Reorder the terms:
(-30 + x)(x + -120) = 0

Reorder the terms:
(-30 + x)(-120 + x) = 0

Multiply (-30 + x) * (-120 + x)
(-30(-120 + x) + x(-120 + x)) = 0
((-120 * -30 + x * -30) + x(-120 + x)) = 0
((3600 + -30x) + x(-120 + x)) = 0
(3600 + -30x + (-120 * x + x * x)) = 0
(3600 + -30x + (-120x + x2)) = 0

Combine like terms: -30x + -120x = -150x
(3600 + -150x + x2) = 0

Solving
3600 + -150x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(30 + -1x)(120 + -1x) = 0

Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Subproblem 2
Set the factor '(120 + -1x)' equal to zero and attempt to solve:

Simplifying
120 + -1x = 0

Solving
120 + -1x = 0

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

Add '-120' to each side of the equation.
120 + -120 + -1x = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -1x = 0 + -120
-1x = 0 + -120

Combine like terms: 0 + -120 = -120
-1x = -120

Divide each side by '-1'.
x = 120

Simplifying
x = 120
Solution
x = {30, 120}