(x-5)(2x-1)=(2x+3)(x+6)

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Solution for (x-5)(2x-1)=(2x+3)(x+6) equation: 


Simplifying
(x + -5)(2x + -1) = (2x + 3)(x + 6)

Reorder the terms:
(-5 + x)(2x + -1) = (2x + 3)(x + 6)

Reorder the terms:
(-5 + x)(-1 + 2x) = (2x + 3)(x + 6)

Multiply (-5 + x) * (-1 + 2x)
(-5(-1 + 2x) + x(-1 + 2x)) = (2x + 3)(x + 6)
((-1 * -5 + 2x * -5) + x(-1 + 2x)) = (2x + 3)(x + 6)
((5 + -10x) + x(-1 + 2x)) = (2x + 3)(x + 6)
(5 + -10x + (-1 * x + 2x * x)) = (2x + 3)(x + 6)
(5 + -10x + (-1x + 2x2)) = (2x + 3)(x + 6)

Combine like terms: -10x + -1x = -11x
(5 + -11x + 2x2) = (2x + 3)(x + 6)

Reorder the terms:
5 + -11x + 2x2 = (3 + 2x)(x + 6)

Reorder the terms:
5 + -11x + 2x2 = (3 + 2x)(6 + x)

Multiply (3 + 2x) * (6 + x)
5 + -11x + 2x2 = (3(6 + x) + 2x * (6 + x))
5 + -11x + 2x2 = ((6 * 3 + x * 3) + 2x * (6 + x))
5 + -11x + 2x2 = ((18 + 3x) + 2x * (6 + x))
5 + -11x + 2x2 = (18 + 3x + (6 * 2x + x * 2x))
5 + -11x + 2x2 = (18 + 3x + (12x + 2x2))

Combine like terms: 3x + 12x = 15x
5 + -11x + 2x2 = (18 + 15x + 2x2)

Add '-2x2' to each side of the equation.
5 + -11x + 2x2 + -2x2 = 18 + 15x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + -11x + 0 = 18 + 15x + 2x2 + -2x2
5 + -11x = 18 + 15x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + -11x = 18 + 15x + 0
5 + -11x = 18 + 15x

Solving
5 + -11x = 18 + 15x

Solving for variable 'x'.

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

Add '-15x' to each side of the equation.
5 + -11x + -15x = 18 + 15x + -15x

Combine like terms: -11x + -15x = -26x
5 + -26x = 18 + 15x + -15x

Combine like terms: 15x + -15x = 0
5 + -26x = 18 + 0
5 + -26x = 18

Add '-5' to each side of the equation.
5 + -5 + -26x = 18 + -5

Combine like terms: 5 + -5 = 0
0 + -26x = 18 + -5
-26x = 18 + -5

Combine like terms: 18 + -5 = 13
-26x = 13

Divide each side by '-26'.
x = -0.5

Simplifying
x = -0.5

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