(x+2x-120)(x+2x-120)=0

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Solution for (x+2x-120)(x+2x-120)=0 equation: 


Simplifying
(x + 2x + -120)(x + 2x + -120) = 0

Reorder the terms:
(-120 + x + 2x)(x + 2x + -120) = 0

Combine like terms: x + 2x = 3x
(-120 + 3x)(x + 2x + -120) = 0

Reorder the terms:
(-120 + 3x)(-120 + x + 2x) = 0

Combine like terms: x + 2x = 3x
(-120 + 3x)(-120 + 3x) = 0

Multiply (-120 + 3x) * (-120 + 3x)
(-120(-120 + 3x) + 3x * (-120 + 3x)) = 0
((-120 * -120 + 3x * -120) + 3x * (-120 + 3x)) = 0
((14400 + -360x) + 3x * (-120 + 3x)) = 0
(14400 + -360x + (-120 * 3x + 3x * 3x)) = 0
(14400 + -360x + (-360x + 9x2)) = 0

Combine like terms: -360x + -360x = -720x
(14400 + -720x + 9x2) = 0

Solving
14400 + -720x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(1600 + -80x + x2) = 0

Factor a trinomial.
9((40 + -1x)(40 + -1x)) = 0

Ignore the factor 9.

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 '(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
Solution
x = {40, 40}

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