(x+120)(144)+144x=x(x+120)

Solution for (x+120)(144)+144x=x(x+120) equation:

Simplifying
(x + 120)(144) + 144x = x(x + 120)

Reorder the terms:
(120 + x)(144) + 144x = x(x + 120)

Reorder the terms for easier multiplication:
144(120 + x) + 144x = x(x + 120)
(120 * 144 + x * 144) + 144x = x(x + 120)
(17280 + 144x) + 144x = x(x + 120)

Combine like terms: 144x + 144x = 288x
17280 + 288x = x(x + 120)

Reorder the terms:
17280 + 288x = x(120 + x)
17280 + 288x = (120 * x + x * x)
17280 + 288x = (120x + x2)

Solving
17280 + 288x = 120x + x2

Solving for variable 'x'.

Combine like terms: 288x + -120x = 168x
17280 + 168x + -1x2 = 120x + x2 + -120x + -1x2

Reorder the terms:
17280 + 168x + -1x2 = 120x + -120x + x2 + -1x2

Combine like terms: 120x + -120x = 0
17280 + 168x + -1x2 = 0 + x2 + -1x2
17280 + 168x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
17280 + 168x + -1x2 = 0

Factor a trinomial.
(240 + -1x)(72 + x) = 0

Subproblem 1
Set the factor '(240 + -1x)' equal to zero and attempt to solve:

Simplifying
240 + -1x = 0

Solving
240 + -1x = 0

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

Add '-240' to each side of the equation.
240 + -240 + -1x = 0 + -240

Combine like terms: 240 + -240 = 0
0 + -1x = 0 + -240
-1x = 0 + -240

Combine like terms: 0 + -240 = -240
-1x = -240

Divide each side by '-1'.
x = 240

Simplifying
x = 240
Subproblem 2
Set the factor '(72 + x)' equal to zero and attempt to solve:

Simplifying
72 + x = 0

Solving
72 + x = 0

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

Add '-72' to each side of the equation.
72 + -72 + x = 0 + -72

Combine like terms: 72 + -72 = 0
0 + x = 0 + -72
x = 0 + -72

Combine like terms: 0 + -72 = -72
x = -72

Simplifying
x = -72
Solution
x = {240, -72}