(20+2x)(40+2x)=1500

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Solution for (20+2x)(40+2x)=1500 equation: 


Simplifying
(20 + 2x)(40 + 2x) = 1500

Multiply (20 + 2x) * (40 + 2x)
(20(40 + 2x) + 2x * (40 + 2x)) = 1500
((40 * 20 + 2x * 20) + 2x * (40 + 2x)) = 1500
((800 + 40x) + 2x * (40 + 2x)) = 1500
(800 + 40x + (40 * 2x + 2x * 2x)) = 1500
(800 + 40x + (80x + 4x2)) = 1500

Combine like terms: 40x + 80x = 120x
(800 + 120x + 4x2) = 1500

Solving
800 + 120x + 4x2 = 1500

Solving for variable 'x'.

Reorder the terms:
800 + -1500 + 120x + 4x2 = 1500 + -1500

Combine like terms: 800 + -1500 = -700
-700 + 120x + 4x2 = 1500 + -1500

Combine like terms: 1500 + -1500 = 0
-700 + 120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-175 + 30x + x2) = 0

Factor a trinomial.
4((-35 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-35 + -1x)' equal to zero and attempt to solve:

Simplifying
-35 + -1x = 0

Solving
-35 + -1x = 0

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

Add '35' to each side of the equation.
-35 + 35 + -1x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -1x = 0 + 35
-1x = 0 + 35

Combine like terms: 0 + 35 = 35
-1x = 35

Divide each side by '-1'.
x = -35

Simplifying
x = -35

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-35, 5}

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