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

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


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

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

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

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

Multiply (9 + 2x) * (-4 + x)
-5x + 2x2 = (9(-4 + x) + 2x * (-4 + x))
-5x + 2x2 = ((-4 * 9 + x * 9) + 2x * (-4 + x))
-5x + 2x2 = ((-36 + 9x) + 2x * (-4 + x))
-5x + 2x2 = (-36 + 9x + (-4 * 2x + x * 2x))
-5x + 2x2 = (-36 + 9x + (-8x + 2x2))

Combine like terms: 9x + -8x = 1x
-5x + 2x2 = (-36 + 1x + 2x2)

Add '-2x2' to each side of the equation.
-5x + 2x2 + -2x2 = -36 + 1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5x + 0 = -36 + 1x + 2x2 + -2x2
-5x = -36 + 1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5x = -36 + 1x + 0
-5x = -36 + 1x

Solving
-5x = -36 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
-5x + -1x = -36 + 1x + -1x

Combine like terms: -5x + -1x = -6x
-6x = -36 + 1x + -1x

Combine like terms: 1x + -1x = 0
-6x = -36 + 0
-6x = -36

Divide each side by '-6'.
x = 6

Simplifying
x = 6

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