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

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


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

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

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

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

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

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

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

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

Combine like terms: -4x + 1x = -3x
-15 + 1x + 2x2 = (-2 + -3x + 2x2)

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

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

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

Solving
-15 + 1x = -2 + -3x

Solving for variable 'x'.

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

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

Combine like terms: 1x + 3x = 4x
-15 + 4x = -2 + -3x + 3x

Combine like terms: -3x + 3x = 0
-15 + 4x = -2 + 0
-15 + 4x = -2

Add '15' to each side of the equation.
-15 + 15 + 4x = -2 + 15

Combine like terms: -15 + 15 = 0
0 + 4x = -2 + 15
4x = -2 + 15

Combine like terms: -2 + 15 = 13
4x = 13

Divide each side by '4'.
x = 3.25

Simplifying
x = 3.25

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