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

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


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

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

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

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

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

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

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

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

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

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

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

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

Solving
-2 + -3x = -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.
-2 + -3x + 4x = -16 + -4x + 4x

Combine like terms: -3x + 4x = 1x
-2 + 1x = -16 + -4x + 4x

Combine like terms: -4x + 4x = 0
-2 + 1x = -16 + 0
-2 + 1x = -16

Add '2' to each side of the equation.
-2 + 2 + 1x = -16 + 2

Combine like terms: -2 + 2 = 0
0 + 1x = -16 + 2
1x = -16 + 2

Combine like terms: -16 + 2 = -14
1x = -14

Divide each side by '1'.
x = -14

Simplifying
x = -14

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