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

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


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

Reorder the terms:
x(-3 + 2x) + x(2x + -2) = (4x + 1)(x + -2)
(-3 * x + 2x * x) + x(2x + -2) = (4x + 1)(x + -2)
(-3x + 2x2) + x(2x + -2) = (4x + 1)(x + -2)

Reorder the terms:
-3x + 2x2 + x(-2 + 2x) = (4x + 1)(x + -2)
-3x + 2x2 + (-2 * x + 2x * x) = (4x + 1)(x + -2)
-3x + 2x2 + (-2x + 2x2) = (4x + 1)(x + -2)

Reorder the terms:
-3x + -2x + 2x2 + 2x2 = (4x + 1)(x + -2)

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

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

Reorder the terms:
-5x + 4x2 = (1 + 4x)(x + -2)

Reorder the terms:
-5x + 4x2 = (1 + 4x)(-2 + x)

Multiply (1 + 4x) * (-2 + x)
-5x + 4x2 = (1(-2 + x) + 4x * (-2 + x))
-5x + 4x2 = ((-2 * 1 + x * 1) + 4x * (-2 + x))
-5x + 4x2 = ((-2 + 1x) + 4x * (-2 + x))
-5x + 4x2 = (-2 + 1x + (-2 * 4x + x * 4x))
-5x + 4x2 = (-2 + 1x + (-8x + 4x2))

Combine like terms: 1x + -8x = -7x
-5x + 4x2 = (-2 + -7x + 4x2)

Add '-4x2' to each side of the equation.
-5x + 4x2 + -4x2 = -2 + -7x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5x + 0 = -2 + -7x + 4x2 + -4x2
-5x = -2 + -7x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5x = -2 + -7x + 0
-5x = -2 + -7x

Solving
-5x = -2 + -7x

Solving for variable 'x'.

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

Add '7x' to each side of the equation.
-5x + 7x = -2 + -7x + 7x

Combine like terms: -5x + 7x = 2x
2x = -2 + -7x + 7x

Combine like terms: -7x + 7x = 0
2x = -2 + 0
2x = -2

Divide each side by '2'.
x = -1

Simplifying
x = -1

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