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

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


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

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

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

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

Multiply (3 + 2x) * (-5 + x)
-8x + 2x2 = (3(-5 + x) + 2x * (-5 + x))
-8x + 2x2 = ((-5 * 3 + x * 3) + 2x * (-5 + x))
-8x + 2x2 = ((-15 + 3x) + 2x * (-5 + x))
-8x + 2x2 = (-15 + 3x + (-5 * 2x + x * 2x))
-8x + 2x2 = (-15 + 3x + (-10x + 2x2))

Combine like terms: 3x + -10x = -7x
-8x + 2x2 = (-15 + -7x + 2x2)

Add '-2x2' to each side of the equation.
-8x + 2x2 + -2x2 = -15 + -7x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8x + 0 = -15 + -7x + 2x2 + -2x2
-8x = -15 + -7x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8x = -15 + -7x + 0
-8x = -15 + -7x

Solving
-8x = -15 + -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 = -15 + -7x + 7x

Combine like terms: -8x + 7x = -1x
-1x = -15 + -7x + 7x

Combine like terms: -7x + 7x = 0
-1x = -15 + 0
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15

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