(2x+200)(2x+300)=81600

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Solution for (2x+200)(2x+300)=81600 equation: 


Simplifying
(2x + 200)(2x + 300) = 81600

Reorder the terms:
(200 + 2x)(2x + 300) = 81600

Reorder the terms:
(200 + 2x)(300 + 2x) = 81600

Multiply (200 + 2x) * (300 + 2x)
(200(300 + 2x) + 2x * (300 + 2x)) = 81600
((300 * 200 + 2x * 200) + 2x * (300 + 2x)) = 81600
((60000 + 400x) + 2x * (300 + 2x)) = 81600
(60000 + 400x + (300 * 2x + 2x * 2x)) = 81600
(60000 + 400x + (600x + 4x2)) = 81600

Combine like terms: 400x + 600x = 1000x
(60000 + 1000x + 4x2) = 81600

Solving
60000 + 1000x + 4x2 = 81600

Solving for variable 'x'.

Reorder the terms:
60000 + -81600 + 1000x + 4x2 = 81600 + -81600

Combine like terms: 60000 + -81600 = -21600
-21600 + 1000x + 4x2 = 81600 + -81600

Combine like terms: 81600 + -81600 = 0
-21600 + 1000x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5400 + 250x + x2) = 0

Factor a trinomial.
4((-270 + -1x)(20 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-270 + -1x)' equal to zero and attempt to solve:

Simplifying
-270 + -1x = 0

Solving
-270 + -1x = 0

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

Add '270' to each side of the equation.
-270 + 270 + -1x = 0 + 270

Combine like terms: -270 + 270 = 0
0 + -1x = 0 + 270
-1x = 0 + 270

Combine like terms: 0 + 270 = 270
-1x = 270

Divide each side by '-1'.
x = -270

Simplifying
x = -270

Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

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

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

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-270, 20}

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