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

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


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

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

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

Multiply (3 + x) * (-5 + 2x)
(3(-5 + 2x) + x(-5 + 2x)) = (2x + -3)(x + 1)
((-5 * 3 + 2x * 3) + x(-5 + 2x)) = (2x + -3)(x + 1)
((-15 + 6x) + x(-5 + 2x)) = (2x + -3)(x + 1)
(-15 + 6x + (-5 * x + 2x * x)) = (2x + -3)(x + 1)
(-15 + 6x + (-5x + 2x2)) = (2x + -3)(x + 1)

Combine like terms: 6x + -5x = 1x
(-15 + 1x + 2x2) = (2x + -3)(x + 1)

Reorder the terms:
-15 + 1x + 2x2 = (-3 + 2x)(x + 1)

Reorder the terms:
-15 + 1x + 2x2 = (-3 + 2x)(1 + x)

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

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

Add '-2x2' to each side of the equation.
-15 + 1x + 2x2 + -2x2 = -3 + -1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 1x + 0 = -3 + -1x + 2x2 + -2x2
-15 + 1x = -3 + -1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 1x = -3 + -1x + 0
-15 + 1x = -3 + -1x

Solving
-15 + 1x = -3 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
-15 + 1x + x = -3 + -1x + x

Combine like terms: 1x + x = 2x
-15 + 2x = -3 + -1x + x

Combine like terms: -1x + x = 0
-15 + 2x = -3 + 0
-15 + 2x = -3

Add '15' to each side of the equation.
-15 + 15 + 2x = -3 + 15

Combine like terms: -15 + 15 = 0
0 + 2x = -3 + 15
2x = -3 + 15

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

Divide each side by '2'.
x = 6

Simplifying
x = 6

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