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

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


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

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

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

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

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

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

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

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

Multiply (2 + 5x) * (-2 + x)
-4x + 5x2 = (2(-2 + x) + 5x * (-2 + x))
-4x + 5x2 = ((-2 * 2 + x * 2) + 5x * (-2 + x))
-4x + 5x2 = ((-4 + 2x) + 5x * (-2 + x))
-4x + 5x2 = (-4 + 2x + (-2 * 5x + x * 5x))
-4x + 5x2 = (-4 + 2x + (-10x + 5x2))

Combine like terms: 2x + -10x = -8x
-4x + 5x2 = (-4 + -8x + 5x2)

Add '-5x2' to each side of the equation.
-4x + 5x2 + -5x2 = -4 + -8x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-4x + 0 = -4 + -8x + 5x2 + -5x2
-4x = -4 + -8x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-4x = -4 + -8x + 0
-4x = -4 + -8x

Solving
-4x = -4 + -8x

Solving for variable 'x'.

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

Add '8x' to each side of the equation.
-4x + 8x = -4 + -8x + 8x

Combine like terms: -4x + 8x = 4x
4x = -4 + -8x + 8x

Combine like terms: -8x + 8x = 0
4x = -4 + 0
4x = -4

Divide each side by '4'.
x = -1

Simplifying
x = -1

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