(120+2x)(70+2x)=15000

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Solution for (120+2x)(70+2x)=15000 equation: 


Simplifying
(120 + 2x)(70 + 2x) = 15000

Multiply (120 + 2x) * (70 + 2x)
(120(70 + 2x) + 2x * (70 + 2x)) = 15000
((70 * 120 + 2x * 120) + 2x * (70 + 2x)) = 15000
((8400 + 240x) + 2x * (70 + 2x)) = 15000
(8400 + 240x + (70 * 2x + 2x * 2x)) = 15000
(8400 + 240x + (140x + 4x2)) = 15000

Combine like terms: 240x + 140x = 380x
(8400 + 380x + 4x2) = 15000

Solving
8400 + 380x + 4x2 = 15000

Solving for variable 'x'.

Reorder the terms:
8400 + -15000 + 380x + 4x2 = 15000 + -15000

Combine like terms: 8400 + -15000 = -6600
-6600 + 380x + 4x2 = 15000 + -15000

Combine like terms: 15000 + -15000 = 0
-6600 + 380x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1650 + 95x + x2) = 0

Factor a trinomial.
4((-110 + -1x)(15 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-110 + -1x)' equal to zero and attempt to solve:

Simplifying
-110 + -1x = 0

Solving
-110 + -1x = 0

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

Add '110' to each side of the equation.
-110 + 110 + -1x = 0 + 110

Combine like terms: -110 + 110 = 0
0 + -1x = 0 + 110
-1x = 0 + 110

Combine like terms: 0 + 110 = 110
-1x = 110

Divide each side by '-1'.
x = -110

Simplifying
x = -110

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-110, 15}

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