x(2x-9)=(2x+5)(x-6)

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Solution for x(2x-9)=(2x+5)(x-6) equation:


Simplifying
x(2x + -9) = (2x + 5)(x + -6)

Reorder the terms:
x(-9 + 2x) = (2x + 5)(x + -6)
(-9 * x + 2x * x) = (2x + 5)(x + -6)
(-9x + 2x2) = (2x + 5)(x + -6)

Reorder the terms:
-9x + 2x2 = (5 + 2x)(x + -6)

Reorder the terms:
-9x + 2x2 = (5 + 2x)(-6 + x)

Multiply (5 + 2x) * (-6 + x)
-9x + 2x2 = (5(-6 + x) + 2x * (-6 + x))
-9x + 2x2 = ((-6 * 5 + x * 5) + 2x * (-6 + x))
-9x + 2x2 = ((-30 + 5x) + 2x * (-6 + x))
-9x + 2x2 = (-30 + 5x + (-6 * 2x + x * 2x))
-9x + 2x2 = (-30 + 5x + (-12x + 2x2))

Combine like terms: 5x + -12x = -7x
-9x + 2x2 = (-30 + -7x + 2x2)

Add '-2x2' to each side of the equation.
-9x + 2x2 + -2x2 = -30 + -7x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-9x + 0 = -30 + -7x + 2x2 + -2x2
-9x = -30 + -7x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-9x = -30 + -7x + 0
-9x = -30 + -7x

Solving
-9x = -30 + -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.
-9x + 7x = -30 + -7x + 7x

Combine like terms: -9x + 7x = -2x
-2x = -30 + -7x + 7x

Combine like terms: -7x + 7x = 0
-2x = -30 + 0
-2x = -30

Divide each side by '-2'.
x = 15

Simplifying
x = 15

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