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

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


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

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

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

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

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

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

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

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

Multiply (6 + 4x) * (-6 + x)
-6x + 4x2 = (6(-6 + x) + 4x * (-6 + x))
-6x + 4x2 = ((-6 * 6 + x * 6) + 4x * (-6 + x))
-6x + 4x2 = ((-36 + 6x) + 4x * (-6 + x))
-6x + 4x2 = (-36 + 6x + (-6 * 4x + x * 4x))
-6x + 4x2 = (-36 + 6x + (-24x + 4x2))

Combine like terms: 6x + -24x = -18x
-6x + 4x2 = (-36 + -18x + 4x2)

Add '-4x2' to each side of the equation.
-6x + 4x2 + -4x2 = -36 + -18x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6x + 0 = -36 + -18x + 4x2 + -4x2
-6x = -36 + -18x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6x = -36 + -18x + 0
-6x = -36 + -18x

Solving
-6x = -36 + -18x

Solving for variable 'x'.

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

Add '18x' to each side of the equation.
-6x + 18x = -36 + -18x + 18x

Combine like terms: -6x + 18x = 12x
12x = -36 + -18x + 18x

Combine like terms: -18x + 18x = 0
12x = -36 + 0
12x = -36

Divide each side by '12'.
x = -3

Simplifying
x = -3

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