(5x+2)(3x-4)=15(x+1)(x-1)-13x

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Solution for (5x+2)(3x-4)=15(x+1)(x-1)-13x equation: 


Simplifying
(5x + 2)(3x + -4) = 15(x + 1)(x + -1) + -13x

Reorder the terms:
(2 + 5x)(3x + -4) = 15(x + 1)(x + -1) + -13x

Reorder the terms:
(2 + 5x)(-4 + 3x) = 15(x + 1)(x + -1) + -13x

Multiply (2 + 5x) * (-4 + 3x)
(2(-4 + 3x) + 5x * (-4 + 3x)) = 15(x + 1)(x + -1) + -13x
((-4 * 2 + 3x * 2) + 5x * (-4 + 3x)) = 15(x + 1)(x + -1) + -13x
((-8 + 6x) + 5x * (-4 + 3x)) = 15(x + 1)(x + -1) + -13x
(-8 + 6x + (-4 * 5x + 3x * 5x)) = 15(x + 1)(x + -1) + -13x
(-8 + 6x + (-20x + 15x2)) = 15(x + 1)(x + -1) + -13x

Combine like terms: 6x + -20x = -14x
(-8 + -14x + 15x2) = 15(x + 1)(x + -1) + -13x

Reorder the terms:
-8 + -14x + 15x2 = 15(1 + x)(x + -1) + -13x

Reorder the terms:
-8 + -14x + 15x2 = 15(1 + x)(-1 + x) + -13x

Multiply (1 + x) * (-1 + x)
-8 + -14x + 15x2 = 15(1(-1 + x) + x(-1 + x)) + -13x
-8 + -14x + 15x2 = 15((-1 * 1 + x * 1) + x(-1 + x)) + -13x
-8 + -14x + 15x2 = 15((-1 + 1x) + x(-1 + x)) + -13x
-8 + -14x + 15x2 = 15(-1 + 1x + (-1 * x + x * x)) + -13x
-8 + -14x + 15x2 = 15(-1 + 1x + (-1x + x2)) + -13x

Combine like terms: 1x + -1x = 0
-8 + -14x + 15x2 = 15(-1 + 0 + x2) + -13x
-8 + -14x + 15x2 = 15(-1 + x2) + -13x
-8 + -14x + 15x2 = (-1 * 15 + x2 * 15) + -13x
-8 + -14x + 15x2 = (-15 + 15x2) + -13x

Reorder the terms:
-8 + -14x + 15x2 = -15 + -13x + 15x2

Add '-15x2' to each side of the equation.
-8 + -14x + 15x2 + -15x2 = -15 + -13x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-8 + -14x + 0 = -15 + -13x + 15x2 + -15x2
-8 + -14x = -15 + -13x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-8 + -14x = -15 + -13x + 0
-8 + -14x = -15 + -13x

Solving
-8 + -14x = -15 + -13x

Solving for variable 'x'.

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

Add '13x' to each side of the equation.
-8 + -14x + 13x = -15 + -13x + 13x

Combine like terms: -14x + 13x = -1x
-8 + -1x = -15 + -13x + 13x

Combine like terms: -13x + 13x = 0
-8 + -1x = -15 + 0
-8 + -1x = -15

Add '8' to each side of the equation.
-8 + 8 + -1x = -15 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = -15 + 8
-1x = -15 + 8

Combine like terms: -15 + 8 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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