x(2x-2)+x(3x-4)=(5x+6)(x-4)

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Solution for x(2x-2)+x(3x-4)=(5x+6)(x-4) equation:


Simplifying
x(2x + -2) + x(3x + -4) = (5x + 6)(x + -4)

Reorder the terms:
x(-2 + 2x) + x(3x + -4) = (5x + 6)(x + -4)
(-2 * x + 2x * x) + x(3x + -4) = (5x + 6)(x + -4)
(-2x + 2x2) + x(3x + -4) = (5x + 6)(x + -4)

Reorder the terms:
-2x + 2x2 + x(-4 + 3x) = (5x + 6)(x + -4)
-2x + 2x2 + (-4 * x + 3x * x) = (5x + 6)(x + -4)
-2x + 2x2 + (-4x + 3x2) = (5x + 6)(x + -4)

Reorder the terms:
-2x + -4x + 2x2 + 3x2 = (5x + 6)(x + -4)

Combine like terms: -2x + -4x = -6x
-6x + 2x2 + 3x2 = (5x + 6)(x + -4)

Combine like terms: 2x2 + 3x2 = 5x2
-6x + 5x2 = (5x + 6)(x + -4)

Reorder the terms:
-6x + 5x2 = (6 + 5x)(x + -4)

Reorder the terms:
-6x + 5x2 = (6 + 5x)(-4 + x)

Multiply (6 + 5x) * (-4 + x)
-6x + 5x2 = (6(-4 + x) + 5x * (-4 + x))
-6x + 5x2 = ((-4 * 6 + x * 6) + 5x * (-4 + x))
-6x + 5x2 = ((-24 + 6x) + 5x * (-4 + x))
-6x + 5x2 = (-24 + 6x + (-4 * 5x + x * 5x))
-6x + 5x2 = (-24 + 6x + (-20x + 5x2))

Combine like terms: 6x + -20x = -14x
-6x + 5x2 = (-24 + -14x + 5x2)

Add '-5x2' to each side of the equation.
-6x + 5x2 + -5x2 = -24 + -14x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-6x + 0 = -24 + -14x + 5x2 + -5x2
-6x = -24 + -14x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-6x = -24 + -14x + 0
-6x = -24 + -14x

Solving
-6x = -24 + -14x

Solving for variable 'x'.

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

Add '14x' to each side of the equation.
-6x + 14x = -24 + -14x + 14x

Combine like terms: -6x + 14x = 8x
8x = -24 + -14x + 14x

Combine like terms: -14x + 14x = 0
8x = -24 + 0
8x = -24

Divide each side by '8'.
x = -3

Simplifying
x = -3

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