x(2x-3)+x(2x-3)=(4x+9)(x-5)

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Solution for x(2x-3)+x(2x-3)=(4x+9)(x-5) equation: 


Simplifying
x(2x + -3) + x(2x + -3) = (4x + 9)(x + -5)

Reorder the terms:
x(-3 + 2x) + x(2x + -3) = (4x + 9)(x + -5)
(-3 * x + 2x * x) + x(2x + -3) = (4x + 9)(x + -5)
(-3x + 2x2) + x(2x + -3) = (4x + 9)(x + -5)

Reorder the terms:
-3x + 2x2 + x(-3 + 2x) = (4x + 9)(x + -5)
-3x + 2x2 + (-3 * x + 2x * x) = (4x + 9)(x + -5)
-3x + 2x2 + (-3x + 2x2) = (4x + 9)(x + -5)

Reorder the terms:
-3x + -3x + 2x2 + 2x2 = (4x + 9)(x + -5)

Combine like terms: -3x + -3x = -6x
-6x + 2x2 + 2x2 = (4x + 9)(x + -5)

Combine like terms: 2x2 + 2x2 = 4x2
-6x + 4x2 = (4x + 9)(x + -5)

Reorder the terms:
-6x + 4x2 = (9 + 4x)(x + -5)

Reorder the terms:
-6x + 4x2 = (9 + 4x)(-5 + x)

Multiply (9 + 4x) * (-5 + x)
-6x + 4x2 = (9(-5 + x) + 4x * (-5 + x))
-6x + 4x2 = ((-5 * 9 + x * 9) + 4x * (-5 + x))
-6x + 4x2 = ((-45 + 9x) + 4x * (-5 + x))
-6x + 4x2 = (-45 + 9x + (-5 * 4x + x * 4x))
-6x + 4x2 = (-45 + 9x + (-20x + 4x2))

Combine like terms: 9x + -20x = -11x
-6x + 4x2 = (-45 + -11x + 4x2)

Add '-4x2' to each side of the equation.
-6x + 4x2 + -4x2 = -45 + -11x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6x + 0 = -45 + -11x + 4x2 + -4x2
-6x = -45 + -11x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6x = -45 + -11x + 0
-6x = -45 + -11x

Solving
-6x = -45 + -11x

Solving for variable 'x'.

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

Add '11x' to each side of the equation.
-6x + 11x = -45 + -11x + 11x

Combine like terms: -6x + 11x = 5x
5x = -45 + -11x + 11x

Combine like terms: -11x + 11x = 0
5x = -45 + 0
5x = -45

Divide each side by '5'.
x = -9

Simplifying
x = -9

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