x(2x-2)+x(3x-3)=(5x+8)(x-3)

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Solution for x(2x-2)+x(3x-3)=(5x+8)(x-3) equation: 


Simplifying
x(2x + -2) + x(3x + -3) = (5x + 8)(x + -3)

Reorder the terms:
x(-2 + 2x) + x(3x + -3) = (5x + 8)(x + -3)
(-2 * x + 2x * x) + x(3x + -3) = (5x + 8)(x + -3)
(-2x + 2x2) + x(3x + -3) = (5x + 8)(x + -3)

Reorder the terms:
-2x + 2x2 + x(-3 + 3x) = (5x + 8)(x + -3)
-2x + 2x2 + (-3 * x + 3x * x) = (5x + 8)(x + -3)
-2x + 2x2 + (-3x + 3x2) = (5x + 8)(x + -3)

Reorder the terms:
-2x + -3x + 2x2 + 3x2 = (5x + 8)(x + -3)

Combine like terms: -2x + -3x = -5x
-5x + 2x2 + 3x2 = (5x + 8)(x + -3)

Combine like terms: 2x2 + 3x2 = 5x2
-5x + 5x2 = (5x + 8)(x + -3)

Reorder the terms:
-5x + 5x2 = (8 + 5x)(x + -3)

Reorder the terms:
-5x + 5x2 = (8 + 5x)(-3 + x)

Multiply (8 + 5x) * (-3 + x)
-5x + 5x2 = (8(-3 + x) + 5x * (-3 + x))
-5x + 5x2 = ((-3 * 8 + x * 8) + 5x * (-3 + x))
-5x + 5x2 = ((-24 + 8x) + 5x * (-3 + x))
-5x + 5x2 = (-24 + 8x + (-3 * 5x + x * 5x))
-5x + 5x2 = (-24 + 8x + (-15x + 5x2))

Combine like terms: 8x + -15x = -7x
-5x + 5x2 = (-24 + -7x + 5x2)

Add '-5x2' to each side of the equation.
-5x + 5x2 + -5x2 = -24 + -7x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-5x + 0 = -24 + -7x + 5x2 + -5x2
-5x = -24 + -7x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-5x = -24 + -7x + 0
-5x = -24 + -7x

Solving
-5x = -24 + -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 = -24 + -7x + 7x

Combine like terms: -5x + 7x = 2x
2x = -24 + -7x + 7x

Combine like terms: -7x + 7x = 0
2x = -24 + 0
2x = -24

Divide each side by '2'.
x = -12

Simplifying
x = -12

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