(10+2x)(15+2x)=500

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Solution for (10+2x)(15+2x)=500 equation: 


Simplifying
(10 + 2x)(15 + 2x) = 500

Multiply (10 + 2x) * (15 + 2x)
(10(15 + 2x) + 2x * (15 + 2x)) = 500
((15 * 10 + 2x * 10) + 2x * (15 + 2x)) = 500
((150 + 20x) + 2x * (15 + 2x)) = 500
(150 + 20x + (15 * 2x + 2x * 2x)) = 500
(150 + 20x + (30x + 4x2)) = 500

Combine like terms: 20x + 30x = 50x
(150 + 50x + 4x2) = 500

Solving
150 + 50x + 4x2 = 500

Solving for variable 'x'.

Reorder the terms:
150 + -500 + 50x + 4x2 = 500 + -500

Combine like terms: 150 + -500 = -350
-350 + 50x + 4x2 = 500 + -500

Combine like terms: 500 + -500 = 0
-350 + 50x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-175 + 25x + 2x2) = 0

Factor a trinomial.
2((-35 + -2x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + -2x)' equal to zero and attempt to solve:

Simplifying
-35 + -2x = 0

Solving
-35 + -2x = 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 + -2x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -2x = 0 + 35
-2x = 0 + 35

Combine like terms: 0 + 35 = 35
-2x = 35

Divide each side by '-2'.
x = -17.5

Simplifying
x = -17.5

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 = {-17.5, 5}

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