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

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


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

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

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

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

Combine like terms: -3x + -5x = -8x
-8x + 2x2 + 2x2 = (4x + 9)(x + -4)

Combine like terms: 2x2 + 2x2 = 4x2
-8x + 4x2 = (4x + 9)(x + -4)

Reorder the terms:
-8x + 4x2 = (9 + 4x)(x + -4)

Reorder the terms:
-8x + 4x2 = (9 + 4x)(-4 + x)

Multiply (9 + 4x) * (-4 + x)
-8x + 4x2 = (9(-4 + x) + 4x * (-4 + x))
-8x + 4x2 = ((-4 * 9 + x * 9) + 4x * (-4 + x))
-8x + 4x2 = ((-36 + 9x) + 4x * (-4 + x))
-8x + 4x2 = (-36 + 9x + (-4 * 4x + x * 4x))
-8x + 4x2 = (-36 + 9x + (-16x + 4x2))

Combine like terms: 9x + -16x = -7x
-8x + 4x2 = (-36 + -7x + 4x2)

Add '-4x2' to each side of the equation.
-8x + 4x2 + -4x2 = -36 + -7x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8x + 0 = -36 + -7x + 4x2 + -4x2
-8x = -36 + -7x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8x = -36 + -7x + 0
-8x = -36 + -7x

Solving
-8x = -36 + -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.
-8x + 7x = -36 + -7x + 7x

Combine like terms: -8x + 7x = -1x
-1x = -36 + -7x + 7x

Combine like terms: -7x + 7x = 0
-1x = -36 + 0
-1x = -36

Divide each side by '-1'.
x = 36

Simplifying
x = 36

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