x(2x-2)+x(2x-6)=(4x+7)(x-2)

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Solution for x(2x-2)+x(2x-6)=(4x+7)(x-2) equation: 


Simplifying
x(2x + -2) + x(2x + -6) = (4x + 7)(x + -2)

Reorder the terms:
x(-2 + 2x) + x(2x + -6) = (4x + 7)(x + -2)
(-2 * x + 2x * x) + x(2x + -6) = (4x + 7)(x + -2)
(-2x + 2x2) + x(2x + -6) = (4x + 7)(x + -2)

Reorder the terms:
-2x + 2x2 + x(-6 + 2x) = (4x + 7)(x + -2)
-2x + 2x2 + (-6 * x + 2x * x) = (4x + 7)(x + -2)
-2x + 2x2 + (-6x + 2x2) = (4x + 7)(x + -2)

Reorder the terms:
-2x + -6x + 2x2 + 2x2 = (4x + 7)(x + -2)

Combine like terms: -2x + -6x = -8x
-8x + 2x2 + 2x2 = (4x + 7)(x + -2)

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

Reorder the terms:
-8x + 4x2 = (7 + 4x)(x + -2)

Reorder the terms:
-8x + 4x2 = (7 + 4x)(-2 + x)

Multiply (7 + 4x) * (-2 + x)
-8x + 4x2 = (7(-2 + x) + 4x * (-2 + x))
-8x + 4x2 = ((-2 * 7 + x * 7) + 4x * (-2 + x))
-8x + 4x2 = ((-14 + 7x) + 4x * (-2 + x))
-8x + 4x2 = (-14 + 7x + (-2 * 4x + x * 4x))
-8x + 4x2 = (-14 + 7x + (-8x + 4x2))

Combine like terms: 7x + -8x = -1x
-8x + 4x2 = (-14 + -1x + 4x2)

Add '-4x2' to each side of the equation.
-8x + 4x2 + -4x2 = -14 + -1x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8x + 0 = -14 + -1x + 4x2 + -4x2
-8x = -14 + -1x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8x = -14 + -1x + 0
-8x = -14 + -1x

Solving
-8x = -14 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
-8x + x = -14 + -1x + x

Combine like terms: -8x + x = -7x
-7x = -14 + -1x + x

Combine like terms: -1x + x = 0
-7x = -14 + 0
-7x = -14

Divide each side by '-7'.
x = 2

Simplifying
x = 2

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