(x-3)(2x+1)=2(x+2)(x-4)

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Solution for (x-3)(2x+1)=2(x+2)(x-4) equation: 


Simplifying
(x + -3)(2x + 1) = 2(x + 2)(x + -4)

Reorder the terms:
(-3 + x)(2x + 1) = 2(x + 2)(x + -4)

Reorder the terms:
(-3 + x)(1 + 2x) = 2(x + 2)(x + -4)

Multiply (-3 + x) * (1 + 2x)
(-3(1 + 2x) + x(1 + 2x)) = 2(x + 2)(x + -4)
((1 * -3 + 2x * -3) + x(1 + 2x)) = 2(x + 2)(x + -4)
((-3 + -6x) + x(1 + 2x)) = 2(x + 2)(x + -4)
(-3 + -6x + (1 * x + 2x * x)) = 2(x + 2)(x + -4)
(-3 + -6x + (1x + 2x2)) = 2(x + 2)(x + -4)

Combine like terms: -6x + 1x = -5x
(-3 + -5x + 2x2) = 2(x + 2)(x + -4)

Reorder the terms:
-3 + -5x + 2x2 = 2(2 + x)(x + -4)

Reorder the terms:
-3 + -5x + 2x2 = 2(2 + x)(-4 + x)

Multiply (2 + x) * (-4 + x)
-3 + -5x + 2x2 = 2(2(-4 + x) + x(-4 + x))
-3 + -5x + 2x2 = 2((-4 * 2 + x * 2) + x(-4 + x))
-3 + -5x + 2x2 = 2((-8 + 2x) + x(-4 + x))
-3 + -5x + 2x2 = 2(-8 + 2x + (-4 * x + x * x))
-3 + -5x + 2x2 = 2(-8 + 2x + (-4x + x2))

Combine like terms: 2x + -4x = -2x
-3 + -5x + 2x2 = 2(-8 + -2x + x2)
-3 + -5x + 2x2 = (-8 * 2 + -2x * 2 + x2 * 2)
-3 + -5x + 2x2 = (-16 + -4x + 2x2)

Add '-2x2' to each side of the equation.
-3 + -5x + 2x2 + -2x2 = -16 + -4x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + -5x + 0 = -16 + -4x + 2x2 + -2x2
-3 + -5x = -16 + -4x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + -5x = -16 + -4x + 0
-3 + -5x = -16 + -4x

Solving
-3 + -5x = -16 + -4x

Solving for variable 'x'.

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

Add '4x' to each side of the equation.
-3 + -5x + 4x = -16 + -4x + 4x

Combine like terms: -5x + 4x = -1x
-3 + -1x = -16 + -4x + 4x

Combine like terms: -4x + 4x = 0
-3 + -1x = -16 + 0
-3 + -1x = -16

Add '3' to each side of the equation.
-3 + 3 + -1x = -16 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = -16 + 3
-1x = -16 + 3

Combine like terms: -16 + 3 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13

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