x(2x-3)+x(5x-5)=(7x+8)(x-2)

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Solution for x(2x-3)+x(5x-5)=(7x+8)(x-2) equation:


Simplifying
x(2x + -3) + x(5x + -5) = (7x + 8)(x + -2)

Reorder the terms:
x(-3 + 2x) + x(5x + -5) = (7x + 8)(x + -2)
(-3 * x + 2x * x) + x(5x + -5) = (7x + 8)(x + -2)
(-3x + 2x2) + x(5x + -5) = (7x + 8)(x + -2)

Reorder the terms:
-3x + 2x2 + x(-5 + 5x) = (7x + 8)(x + -2)
-3x + 2x2 + (-5 * x + 5x * x) = (7x + 8)(x + -2)
-3x + 2x2 + (-5x + 5x2) = (7x + 8)(x + -2)

Reorder the terms:
-3x + -5x + 2x2 + 5x2 = (7x + 8)(x + -2)

Combine like terms: -3x + -5x = -8x
-8x + 2x2 + 5x2 = (7x + 8)(x + -2)

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

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

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

Multiply (8 + 7x) * (-2 + x)
-8x + 7x2 = (8(-2 + x) + 7x * (-2 + x))
-8x + 7x2 = ((-2 * 8 + x * 8) + 7x * (-2 + x))
-8x + 7x2 = ((-16 + 8x) + 7x * (-2 + x))
-8x + 7x2 = (-16 + 8x + (-2 * 7x + x * 7x))
-8x + 7x2 = (-16 + 8x + (-14x + 7x2))

Combine like terms: 8x + -14x = -6x
-8x + 7x2 = (-16 + -6x + 7x2)

Add '-7x2' to each side of the equation.
-8x + 7x2 + -7x2 = -16 + -6x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-8x + 0 = -16 + -6x + 7x2 + -7x2
-8x = -16 + -6x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-8x = -16 + -6x + 0
-8x = -16 + -6x

Solving
-8x = -16 + -6x

Solving for variable 'x'.

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

Add '6x' to each side of the equation.
-8x + 6x = -16 + -6x + 6x

Combine like terms: -8x + 6x = -2x
-2x = -16 + -6x + 6x

Combine like terms: -6x + 6x = 0
-2x = -16 + 0
-2x = -16

Divide each side by '-2'.
x = 8

Simplifying
x = 8

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