(x+5)(x-6)=(x+9)(x-15)

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Solution for (x+5)(x-6)=(x+9)(x-15) equation: 


Simplifying
(x + 5)(x + -6) = (x + 9)(x + -15)

Reorder the terms:
(5 + x)(x + -6) = (x + 9)(x + -15)

Reorder the terms:
(5 + x)(-6 + x) = (x + 9)(x + -15)

Multiply (5 + x) * (-6 + x)
(5(-6 + x) + x(-6 + x)) = (x + 9)(x + -15)
((-6 * 5 + x * 5) + x(-6 + x)) = (x + 9)(x + -15)
((-30 + 5x) + x(-6 + x)) = (x + 9)(x + -15)
(-30 + 5x + (-6 * x + x * x)) = (x + 9)(x + -15)
(-30 + 5x + (-6x + x2)) = (x + 9)(x + -15)

Combine like terms: 5x + -6x = -1x
(-30 + -1x + x2) = (x + 9)(x + -15)

Reorder the terms:
-30 + -1x + x2 = (9 + x)(x + -15)

Reorder the terms:
-30 + -1x + x2 = (9 + x)(-15 + x)

Multiply (9 + x) * (-15 + x)
-30 + -1x + x2 = (9(-15 + x) + x(-15 + x))
-30 + -1x + x2 = ((-15 * 9 + x * 9) + x(-15 + x))
-30 + -1x + x2 = ((-135 + 9x) + x(-15 + x))
-30 + -1x + x2 = (-135 + 9x + (-15 * x + x * x))
-30 + -1x + x2 = (-135 + 9x + (-15x + x2))

Combine like terms: 9x + -15x = -6x
-30 + -1x + x2 = (-135 + -6x + x2)

Add '-1x2' to each side of the equation.
-30 + -1x + x2 + -1x2 = -135 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-30 + -1x + 0 = -135 + -6x + x2 + -1x2
-30 + -1x = -135 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-30 + -1x = -135 + -6x + 0
-30 + -1x = -135 + -6x

Solving
-30 + -1x = -135 + -6x

Solving for variable 'x'.

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

Add '6x' to each side of the equation.
-30 + -1x + 6x = -135 + -6x + 6x

Combine like terms: -1x + 6x = 5x
-30 + 5x = -135 + -6x + 6x

Combine like terms: -6x + 6x = 0
-30 + 5x = -135 + 0
-30 + 5x = -135

Add '30' to each side of the equation.
-30 + 30 + 5x = -135 + 30

Combine like terms: -30 + 30 = 0
0 + 5x = -135 + 30
5x = -135 + 30

Combine like terms: -135 + 30 = -105
5x = -105

Divide each side by '5'.
x = -21

Simplifying
x = -21

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