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

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


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

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

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

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

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

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

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

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

Multiply (8 + 7x) * (-3 + x)
-5x + 7x2 = (8(-3 + x) + 7x * (-3 + x))
-5x + 7x2 = ((-3 * 8 + x * 8) + 7x * (-3 + x))
-5x + 7x2 = ((-24 + 8x) + 7x * (-3 + x))
-5x + 7x2 = (-24 + 8x + (-3 * 7x + x * 7x))
-5x + 7x2 = (-24 + 8x + (-21x + 7x2))

Combine like terms: 8x + -21x = -13x
-5x + 7x2 = (-24 + -13x + 7x2)

Add '-7x2' to each side of the equation.
-5x + 7x2 + -7x2 = -24 + -13x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-5x + 0 = -24 + -13x + 7x2 + -7x2
-5x = -24 + -13x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-5x = -24 + -13x + 0
-5x = -24 + -13x

Solving
-5x = -24 + -13x

Solving for variable 'x'.

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

Add '13x' to each side of the equation.
-5x + 13x = -24 + -13x + 13x

Combine like terms: -5x + 13x = 8x
8x = -24 + -13x + 13x

Combine like terms: -13x + 13x = 0
8x = -24 + 0
8x = -24

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

Simplifying
x = -3

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