(x+5)(x-8)=(x-7)(x-2)

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Solution for (x+5)(x-8)=(x-7)(x-2) equation: 


Simplifying
(x + 5)(x + -8) = (x + -7)(x + -2)

Reorder the terms:
(5 + x)(x + -8) = (x + -7)(x + -2)

Reorder the terms:
(5 + x)(-8 + x) = (x + -7)(x + -2)

Multiply (5 + x) * (-8 + x)
(5(-8 + x) + x(-8 + x)) = (x + -7)(x + -2)
((-8 * 5 + x * 5) + x(-8 + x)) = (x + -7)(x + -2)
((-40 + 5x) + x(-8 + x)) = (x + -7)(x + -2)
(-40 + 5x + (-8 * x + x * x)) = (x + -7)(x + -2)
(-40 + 5x + (-8x + x2)) = (x + -7)(x + -2)

Combine like terms: 5x + -8x = -3x
(-40 + -3x + x2) = (x + -7)(x + -2)

Reorder the terms:
-40 + -3x + x2 = (-7 + x)(x + -2)

Reorder the terms:
-40 + -3x + x2 = (-7 + x)(-2 + x)

Multiply (-7 + x) * (-2 + x)
-40 + -3x + x2 = (-7(-2 + x) + x(-2 + x))
-40 + -3x + x2 = ((-2 * -7 + x * -7) + x(-2 + x))
-40 + -3x + x2 = ((14 + -7x) + x(-2 + x))
-40 + -3x + x2 = (14 + -7x + (-2 * x + x * x))
-40 + -3x + x2 = (14 + -7x + (-2x + x2))

Combine like terms: -7x + -2x = -9x
-40 + -3x + x2 = (14 + -9x + x2)

Add '-1x2' to each side of the equation.
-40 + -3x + x2 + -1x2 = 14 + -9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-40 + -3x + 0 = 14 + -9x + x2 + -1x2
-40 + -3x = 14 + -9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-40 + -3x = 14 + -9x + 0
-40 + -3x = 14 + -9x

Solving
-40 + -3x = 14 + -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.
-40 + -3x + 9x = 14 + -9x + 9x

Combine like terms: -3x + 9x = 6x
-40 + 6x = 14 + -9x + 9x

Combine like terms: -9x + 9x = 0
-40 + 6x = 14 + 0
-40 + 6x = 14

Add '40' to each side of the equation.
-40 + 40 + 6x = 14 + 40

Combine like terms: -40 + 40 = 0
0 + 6x = 14 + 40
6x = 14 + 40

Combine like terms: 14 + 40 = 54
6x = 54

Divide each side by '6'.
x = 9

Simplifying
x = 9

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