(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 = 11x
5 + 7x + 2x2 = (12 + 11x + 2x2)

Add '-2x2' to each side of the equation.
5 + 7x + 2x2 + -2x2 = 12 + 11x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 7x + 0 = 12 + 11x + 2x2 + -2x2
5 + 7x = 12 + 11x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 7x = 12 + 11x + 0
5 + 7x = 12 + 11x

Solving
5 + 7x = 12 + 11x

Solving for variable 'x'.

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

Add '-11x' to each side of the equation.
5 + 7x + -11x = 12 + 11x + -11x

Combine like terms: 7x + -11x = -4x
5 + -4x = 12 + 11x + -11x

Combine like terms: 11x + -11x = 0
5 + -4x = 12 + 0
5 + -4x = 12

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

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

Combine like terms: 12 + -5 = 7
-4x = 7

Divide each side by '-4'.
x = -1.75

Simplifying
x = -1.75

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