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

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


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

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

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

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

Combine like terms: -3x + 10x = 7x
(-15 + 7x + 2x2) = (2x + 1)(x + 2)

Reorder the terms:
-15 + 7x + 2x2 = (1 + 2x)(x + 2)

Reorder the terms:
-15 + 7x + 2x2 = (1 + 2x)(2 + x)

Multiply (1 + 2x) * (2 + x)
-15 + 7x + 2x2 = (1(2 + x) + 2x * (2 + x))
-15 + 7x + 2x2 = ((2 * 1 + x * 1) + 2x * (2 + x))
-15 + 7x + 2x2 = ((2 + 1x) + 2x * (2 + x))
-15 + 7x + 2x2 = (2 + 1x + (2 * 2x + x * 2x))
-15 + 7x + 2x2 = (2 + 1x + (4x + 2x2))

Combine like terms: 1x + 4x = 5x
-15 + 7x + 2x2 = (2 + 5x + 2x2)

Add '-2x2' to each side of the equation.
-15 + 7x + 2x2 + -2x2 = 2 + 5x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 7x + 0 = 2 + 5x + 2x2 + -2x2
-15 + 7x = 2 + 5x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 7x = 2 + 5x + 0
-15 + 7x = 2 + 5x

Solving
-15 + 7x = 2 + 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.
-15 + 7x + -5x = 2 + 5x + -5x

Combine like terms: 7x + -5x = 2x
-15 + 2x = 2 + 5x + -5x

Combine like terms: 5x + -5x = 0
-15 + 2x = 2 + 0
-15 + 2x = 2

Add '15' to each side of the equation.
-15 + 15 + 2x = 2 + 15

Combine like terms: -15 + 15 = 0
0 + 2x = 2 + 15
2x = 2 + 15

Combine like terms: 2 + 15 = 17
2x = 17

Divide each side by '2'.
x = 8.5

Simplifying
x = 8.5

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