x(2x-4)=(2x+5)(x-7)

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Solution for x(2x-4)=(2x+5)(x-7) equation:


Simplifying
x(2x + -4) = (2x + 5)(x + -7)

Reorder the terms:
x(-4 + 2x) = (2x + 5)(x + -7)
(-4 * x + 2x * x) = (2x + 5)(x + -7)
(-4x + 2x2) = (2x + 5)(x + -7)

Reorder the terms:
-4x + 2x2 = (5 + 2x)(x + -7)

Reorder the terms:
-4x + 2x2 = (5 + 2x)(-7 + x)

Multiply (5 + 2x) * (-7 + x)
-4x + 2x2 = (5(-7 + x) + 2x * (-7 + x))
-4x + 2x2 = ((-7 * 5 + x * 5) + 2x * (-7 + x))
-4x + 2x2 = ((-35 + 5x) + 2x * (-7 + x))
-4x + 2x2 = (-35 + 5x + (-7 * 2x + x * 2x))
-4x + 2x2 = (-35 + 5x + (-14x + 2x2))

Combine like terms: 5x + -14x = -9x
-4x + 2x2 = (-35 + -9x + 2x2)

Add '-2x2' to each side of the equation.
-4x + 2x2 + -2x2 = -35 + -9x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4x + 0 = -35 + -9x + 2x2 + -2x2
-4x = -35 + -9x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4x = -35 + -9x + 0
-4x = -35 + -9x

Solving
-4x = -35 + -9x

Solving for variable 'x'.

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

Add '9x' to each side of the equation.
-4x + 9x = -35 + -9x + 9x

Combine like terms: -4x + 9x = 5x
5x = -35 + -9x + 9x

Combine like terms: -9x + 9x = 0
5x = -35 + 0
5x = -35

Divide each side by '5'.
x = -7

Simplifying
x = -7

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