(120+2x)(50+2x)=0

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Solution for (120+2x)(50+2x)=0 equation: 


Simplifying
(120 + 2x)(50 + 2x) = 0

Multiply (120 + 2x) * (50 + 2x)
(120(50 + 2x) + 2x * (50 + 2x)) = 0
((50 * 120 + 2x * 120) + 2x * (50 + 2x)) = 0
((6000 + 240x) + 2x * (50 + 2x)) = 0
(6000 + 240x + (50 * 2x + 2x * 2x)) = 0
(6000 + 240x + (100x + 4x2)) = 0

Combine like terms: 240x + 100x = 340x
(6000 + 340x + 4x2) = 0

Solving
6000 + 340x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1500 + 85x + x2) = 0

Factor a trinomial.
4((60 + x)(25 + x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(25 + x)' equal to zero and attempt to solve:

Simplifying
25 + x = 0

Solving
25 + x = 0

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

Add '-25' to each side of the equation.
25 + -25 + x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + x = 0 + -25
x = 0 + -25

Combine like terms: 0 + -25 = -25
x = -25

Simplifying
x = -25
Solution
x = {-60, -25}

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