(2x+3)(x+5)-(2x+5)(x+3)=0

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Solution for (2x+3)(x+5)-(2x+5)(x+3)=0 equation: 


Simplifying
(2x + 3)(x + 5) + -1(2x + 5)(x + 3) = 0

Reorder the terms:
(3 + 2x)(x + 5) + -1(2x + 5)(x + 3) = 0

Reorder the terms:
(3 + 2x)(5 + x) + -1(2x + 5)(x + 3) = 0

Multiply (3 + 2x) * (5 + x)
(3(5 + x) + 2x * (5 + x)) + -1(2x + 5)(x + 3) = 0
((5 * 3 + x * 3) + 2x * (5 + x)) + -1(2x + 5)(x + 3) = 0
((15 + 3x) + 2x * (5 + x)) + -1(2x + 5)(x + 3) = 0
(15 + 3x + (5 * 2x + x * 2x)) + -1(2x + 5)(x + 3) = 0
(15 + 3x + (10x + 2x2)) + -1(2x + 5)(x + 3) = 0

Combine like terms: 3x + 10x = 13x
(15 + 13x + 2x2) + -1(2x + 5)(x + 3) = 0

Reorder the terms:
15 + 13x + 2x2 + -1(5 + 2x)(x + 3) = 0

Reorder the terms:
15 + 13x + 2x2 + -1(5 + 2x)(3 + x) = 0

Multiply (5 + 2x) * (3 + x)
15 + 13x + 2x2 + -1(5(3 + x) + 2x * (3 + x)) = 0
15 + 13x + 2x2 + -1((3 * 5 + x * 5) + 2x * (3 + x)) = 0
15 + 13x + 2x2 + -1((15 + 5x) + 2x * (3 + x)) = 0
15 + 13x + 2x2 + -1(15 + 5x + (3 * 2x + x * 2x)) = 0
15 + 13x + 2x2 + -1(15 + 5x + (6x + 2x2)) = 0

Combine like terms: 5x + 6x = 11x
15 + 13x + 2x2 + -1(15 + 11x + 2x2) = 0
15 + 13x + 2x2 + (15 * -1 + 11x * -1 + 2x2 * -1) = 0
15 + 13x + 2x2 + (-15 + -11x + -2x2) = 0

Reorder the terms:
15 + -15 + 13x + -11x + 2x2 + -2x2 = 0

Combine like terms: 15 + -15 = 0
0 + 13x + -11x + 2x2 + -2x2 = 0
13x + -11x + 2x2 + -2x2 = 0

Combine like terms: 13x + -11x = 2x
2x + 2x2 + -2x2 = 0

Combine like terms: 2x2 + -2x2 = 0
2x + 0 = 0
2x = 0

Solving
2x = 0

Solving for variable 'x'.

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

Divide each side by '2'.
x = 0

Simplifying
x = 0

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