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

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


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

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

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

Multiply (1 + 2x) * (5 + 2x)
(1(5 + 2x) + 2x * (5 + 2x)) = (2x + 3)(2x + -4) + 15
((5 * 1 + 2x * 1) + 2x * (5 + 2x)) = (2x + 3)(2x + -4) + 15
((5 + 2x) + 2x * (5 + 2x)) = (2x + 3)(2x + -4) + 15
(5 + 2x + (5 * 2x + 2x * 2x)) = (2x + 3)(2x + -4) + 15
(5 + 2x + (10x + 4x2)) = (2x + 3)(2x + -4) + 15

Combine like terms: 2x + 10x = 12x
(5 + 12x + 4x2) = (2x + 3)(2x + -4) + 15

Reorder the terms:
5 + 12x + 4x2 = (3 + 2x)(2x + -4) + 15

Reorder the terms:
5 + 12x + 4x2 = (3 + 2x)(-4 + 2x) + 15

Multiply (3 + 2x) * (-4 + 2x)
5 + 12x + 4x2 = (3(-4 + 2x) + 2x * (-4 + 2x)) + 15
5 + 12x + 4x2 = ((-4 * 3 + 2x * 3) + 2x * (-4 + 2x)) + 15
5 + 12x + 4x2 = ((-12 + 6x) + 2x * (-4 + 2x)) + 15
5 + 12x + 4x2 = (-12 + 6x + (-4 * 2x + 2x * 2x)) + 15
5 + 12x + 4x2 = (-12 + 6x + (-8x + 4x2)) + 15

Combine like terms: 6x + -8x = -2x
5 + 12x + 4x2 = (-12 + -2x + 4x2) + 15

Reorder the terms:
5 + 12x + 4x2 = -12 + 15 + -2x + 4x2

Combine like terms: -12 + 15 = 3
5 + 12x + 4x2 = 3 + -2x + 4x2

Add '-4x2' to each side of the equation.
5 + 12x + 4x2 + -4x2 = 3 + -2x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
5 + 12x + 0 = 3 + -2x + 4x2 + -4x2
5 + 12x = 3 + -2x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
5 + 12x = 3 + -2x + 0
5 + 12x = 3 + -2x

Solving
5 + 12x = 3 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
5 + 12x + 2x = 3 + -2x + 2x

Combine like terms: 12x + 2x = 14x
5 + 14x = 3 + -2x + 2x

Combine like terms: -2x + 2x = 0
5 + 14x = 3 + 0
5 + 14x = 3

Add '-5' to each side of the equation.
5 + -5 + 14x = 3 + -5

Combine like terms: 5 + -5 = 0
0 + 14x = 3 + -5
14x = 3 + -5

Combine like terms: 3 + -5 = -2
14x = -2

Divide each side by '14'.
x = -0.1428571429

Simplifying
x = -0.1428571429

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