0=(x-120)(x+75)

Solution for 0=(x-120)(x+75) equation:

Simplifying
0 = (x + -120)(x + 75)

Reorder the terms:
0 = (-120 + x)(x + 75)

Reorder the terms:
0 = (-120 + x)(75 + x)

Multiply (-120 + x) * (75 + x)
0 = (-120(75 + x) + x(75 + x))
0 = ((75 * -120 + x * -120) + x(75 + x))
0 = ((-9000 + -120x) + x(75 + x))
0 = (-9000 + -120x + (75 * x + x * x))
0 = (-9000 + -120x + (75x + x2))

Combine like terms: -120x + 75x = -45x
0 = (-9000 + -45x + x2)

Solving
0 = -9000 + -45x + x2

Solving for variable 'x'.

Combine like terms: 0 + 9000 = 9000
9000 + 45x + -1x2 = -9000 + -45x + x2 + 9000 + 45x + -1x2

Reorder the terms:
9000 + 45x + -1x2 = -9000 + 9000 + -45x + 45x + x2 + -1x2

Combine like terms: -9000 + 9000 = 0
9000 + 45x + -1x2 = 0 + -45x + 45x + x2 + -1x2
9000 + 45x + -1x2 = -45x + 45x + x2 + -1x2

Combine like terms: -45x + 45x = 0
9000 + 45x + -1x2 = 0 + x2 + -1x2
9000 + 45x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9000 + 45x + -1x2 = 0

Factor a trinomial.
(120 + -1x)(75 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(75 + x)' equal to zero and attempt to solve:

Simplifying
75 + x = 0

Solving
75 + x = 0

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

Add '-75' to each side of the equation.
75 + -75 + x = 0 + -75

Combine like terms: 75 + -75 = 0
0 + x = 0 + -75
x = 0 + -75

Combine like terms: 0 + -75 = -75
x = -75

Simplifying
x = -75
Solution
x = {120, -75}