120(x+20)=120x+x(x+20)

Solution for 120(x+20)=120x+x(x+20) equation:

Simplifying
120(x + 20) = 120x + x(x + 20)

Reorder the terms:
120(20 + x) = 120x + x(x + 20)
(20 * 120 + x * 120) = 120x + x(x + 20)
(2400 + 120x) = 120x + x(x + 20)

Reorder the terms:
2400 + 120x = 120x + x(20 + x)
2400 + 120x = 120x + (20 * x + x * x)
2400 + 120x = 120x + (20x + x2)

Combine like terms: 120x + 20x = 140x
2400 + 120x = 140x + x2

Solving
2400 + 120x = 140x + x2

Solving for variable 'x'.

Combine like terms: 120x + -140x = -20x
2400 + -20x + -1x2 = 140x + x2 + -140x + -1x2

Reorder the terms:
2400 + -20x + -1x2 = 140x + -140x + x2 + -1x2

Combine like terms: 140x + -140x = 0
2400 + -20x + -1x2 = 0 + x2 + -1x2
2400 + -20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2400 + -20x + -1x2 = 0

Factor a trinomial.
(40 + -1x)(60 + x) = 0

Subproblem 1
Set the factor '(40 + -1x)' equal to zero and attempt to solve:

Simplifying
40 + -1x = 0

Solving
40 + -1x = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1x = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1x = 0 + -40
-1x = 0 + -40

Combine like terms: 0 + -40 = -40
-1x = -40

Divide each side by '-1'.
x = 40

Simplifying
x = 40
Subproblem 2
Set the factor '(60 + x)' equal to zero and attempt to solve:

Simplifying
60 + x = 0

Solving
60 + x = 0

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

Add '-60' to each side of the equation.
60 + -60 + x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + x = 0 + -60
x = 0 + -60

Combine like terms: 0 + -60 = -60
x = -60

Simplifying
x = -60
Solution
x = {40, -60}