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

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


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

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

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

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

Combine like terms: 2x + 5x = 7x
(5 + 7x + 2x2) = (2x + 3)(x + -4)

Reorder the terms:
5 + 7x + 2x2 = (3 + 2x)(x + -4)

Reorder the terms:
5 + 7x + 2x2 = (3 + 2x)(-4 + x)

Multiply (3 + 2x) * (-4 + x)
5 + 7x + 2x2 = (3(-4 + x) + 2x * (-4 + x))
5 + 7x + 2x2 = ((-4 * 3 + x * 3) + 2x * (-4 + x))
5 + 7x + 2x2 = ((-12 + 3x) + 2x * (-4 + x))
5 + 7x + 2x2 = (-12 + 3x + (-4 * 2x + x * 2x))
5 + 7x + 2x2 = (-12 + 3x + (-8x + 2x2))

Combine like terms: 3x + -8x = -5x
5 + 7x + 2x2 = (-12 + -5x + 2x2)

Add '-2x2' to each side of the equation.
5 + 7x + 2x2 + -2x2 = -12 + -5x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 7x + 0 = -12 + -5x + 2x2 + -2x2
5 + 7x = -12 + -5x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 7x = -12 + -5x + 0
5 + 7x = -12 + -5x

Solving
5 + 7x = -12 + -5x

Solving for variable 'x'.

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

Add '5x' to each side of the equation.
5 + 7x + 5x = -12 + -5x + 5x

Combine like terms: 7x + 5x = 12x
5 + 12x = -12 + -5x + 5x

Combine like terms: -5x + 5x = 0
5 + 12x = -12 + 0
5 + 12x = -12

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

Combine like terms: 5 + -5 = 0
0 + 12x = -12 + -5
12x = -12 + -5

Combine like terms: -12 + -5 = -17
12x = -17

Divide each side by '12'.
x = -1.416666667

Simplifying
x = -1.416666667

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