(x+2)(x-5)=(x-8)(x+3)

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Solution for (x+2)(x-5)=(x-8)(x+3) equation: 


Simplifying
(x + 2)(x + -5) = (x + -8)(x + 3)

Reorder the terms:
(2 + x)(x + -5) = (x + -8)(x + 3)

Reorder the terms:
(2 + x)(-5 + x) = (x + -8)(x + 3)

Multiply (2 + x) * (-5 + x)
(2(-5 + x) + x(-5 + x)) = (x + -8)(x + 3)
((-5 * 2 + x * 2) + x(-5 + x)) = (x + -8)(x + 3)
((-10 + 2x) + x(-5 + x)) = (x + -8)(x + 3)
(-10 + 2x + (-5 * x + x * x)) = (x + -8)(x + 3)
(-10 + 2x + (-5x + x2)) = (x + -8)(x + 3)

Combine like terms: 2x + -5x = -3x
(-10 + -3x + x2) = (x + -8)(x + 3)

Reorder the terms:
-10 + -3x + x2 = (-8 + x)(x + 3)

Reorder the terms:
-10 + -3x + x2 = (-8 + x)(3 + x)

Multiply (-8 + x) * (3 + x)
-10 + -3x + x2 = (-8(3 + x) + x(3 + x))
-10 + -3x + x2 = ((3 * -8 + x * -8) + x(3 + x))
-10 + -3x + x2 = ((-24 + -8x) + x(3 + x))
-10 + -3x + x2 = (-24 + -8x + (3 * x + x * x))
-10 + -3x + x2 = (-24 + -8x + (3x + x2))

Combine like terms: -8x + 3x = -5x
-10 + -3x + x2 = (-24 + -5x + x2)

Add '-1x2' to each side of the equation.
-10 + -3x + x2 + -1x2 = -24 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x + 0 = -24 + -5x + x2 + -1x2
-10 + -3x = -24 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x = -24 + -5x + 0
-10 + -3x = -24 + -5x

Solving
-10 + -3x = -24 + -5x

Solving for variable 'x'.

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

Add '5x' to each side of the equation.
-10 + -3x + 5x = -24 + -5x + 5x

Combine like terms: -3x + 5x = 2x
-10 + 2x = -24 + -5x + 5x

Combine like terms: -5x + 5x = 0
-10 + 2x = -24 + 0
-10 + 2x = -24

Add '10' to each side of the equation.
-10 + 10 + 2x = -24 + 10

Combine like terms: -10 + 10 = 0
0 + 2x = -24 + 10
2x = -24 + 10

Combine like terms: -24 + 10 = -14
2x = -14

Divide each side by '2'.
x = -7

Simplifying
x = -7

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