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

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


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

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

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

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

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

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

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

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

Multiply (5 + 4x) * (-2 + x)
-5x + 4x2 = (5(-2 + x) + 4x * (-2 + x))
-5x + 4x2 = ((-2 * 5 + x * 5) + 4x * (-2 + x))
-5x + 4x2 = ((-10 + 5x) + 4x * (-2 + x))
-5x + 4x2 = (-10 + 5x + (-2 * 4x + x * 4x))
-5x + 4x2 = (-10 + 5x + (-8x + 4x2))

Combine like terms: 5x + -8x = -3x
-5x + 4x2 = (-10 + -3x + 4x2)

Add '-4x2' to each side of the equation.
-5x + 4x2 + -4x2 = -10 + -3x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5x + 0 = -10 + -3x + 4x2 + -4x2
-5x = -10 + -3x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5x = -10 + -3x + 0
-5x = -10 + -3x

Solving
-5x = -10 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-5x + 3x = -10 + -3x + 3x

Combine like terms: -5x + 3x = -2x
-2x = -10 + -3x + 3x

Combine like terms: -3x + 3x = 0
-2x = -10 + 0
-2x = -10

Divide each side by '-2'.
x = 5

Simplifying
x = 5

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