(x-8)(x-7)=(x-9)(x-5)

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Solution for (x-8)(x-7)=(x-9)(x-5) equation: 


Simplifying
(x + -8)(x + -7) = (x + -9)(x + -5)

Reorder the terms:
(-8 + x)(x + -7) = (x + -9)(x + -5)

Reorder the terms:
(-8 + x)(-7 + x) = (x + -9)(x + -5)

Multiply (-8 + x) * (-7 + x)
(-8(-7 + x) + x(-7 + x)) = (x + -9)(x + -5)
((-7 * -8 + x * -8) + x(-7 + x)) = (x + -9)(x + -5)
((56 + -8x) + x(-7 + x)) = (x + -9)(x + -5)
(56 + -8x + (-7 * x + x * x)) = (x + -9)(x + -5)
(56 + -8x + (-7x + x2)) = (x + -9)(x + -5)

Combine like terms: -8x + -7x = -15x
(56 + -15x + x2) = (x + -9)(x + -5)

Reorder the terms:
56 + -15x + x2 = (-9 + x)(x + -5)

Reorder the terms:
56 + -15x + x2 = (-9 + x)(-5 + x)

Multiply (-9 + x) * (-5 + x)
56 + -15x + x2 = (-9(-5 + x) + x(-5 + x))
56 + -15x + x2 = ((-5 * -9 + x * -9) + x(-5 + x))
56 + -15x + x2 = ((45 + -9x) + x(-5 + x))
56 + -15x + x2 = (45 + -9x + (-5 * x + x * x))
56 + -15x + x2 = (45 + -9x + (-5x + x2))

Combine like terms: -9x + -5x = -14x
56 + -15x + x2 = (45 + -14x + x2)

Add '-1x2' to each side of the equation.
56 + -15x + x2 + -1x2 = 45 + -14x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
56 + -15x + 0 = 45 + -14x + x2 + -1x2
56 + -15x = 45 + -14x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
56 + -15x = 45 + -14x + 0
56 + -15x = 45 + -14x

Solving
56 + -15x = 45 + -14x

Solving for variable 'x'.

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

Add '14x' to each side of the equation.
56 + -15x + 14x = 45 + -14x + 14x

Combine like terms: -15x + 14x = -1x
56 + -1x = 45 + -14x + 14x

Combine like terms: -14x + 14x = 0
56 + -1x = 45 + 0
56 + -1x = 45

Add '-56' to each side of the equation.
56 + -56 + -1x = 45 + -56

Combine like terms: 56 + -56 = 0
0 + -1x = 45 + -56
-1x = 45 + -56

Combine like terms: 45 + -56 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11

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