(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 = 7x
(10 + 7x + x2) = (x + -8)(x + 3)

Reorder the terms:
10 + 7x + x2 = (-8 + x)(x + 3)

Reorder the terms:
10 + 7x + x2 = (-8 + x)(3 + x)

Multiply (-8 + x) * (3 + x)
10 + 7x + x2 = (-8(3 + x) + x(3 + x))
10 + 7x + x2 = ((3 * -8 + x * -8) + x(3 + x))
10 + 7x + x2 = ((-24 + -8x) + x(3 + x))
10 + 7x + x2 = (-24 + -8x + (3 * x + x * x))
10 + 7x + x2 = (-24 + -8x + (3x + x2))

Combine like terms: -8x + 3x = -5x
10 + 7x + x2 = (-24 + -5x + x2)

Add '-1x2' to each side of the equation.
10 + 7x + x2 + -1x2 = -24 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 7x + 0 = -24 + -5x + x2 + -1x2
10 + 7x = -24 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 7x = -24 + -5x + 0
10 + 7x = -24 + -5x

Solving
10 + 7x = -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 + 7x + 5x = -24 + -5x + 5x

Combine like terms: 7x + 5x = 12x
10 + 12x = -24 + -5x + 5x

Combine like terms: -5x + 5x = 0
10 + 12x = -24 + 0
10 + 12x = -24

Add '-10' to each side of the equation.
10 + -10 + 12x = -24 + -10

Combine like terms: 10 + -10 = 0
0 + 12x = -24 + -10
12x = -24 + -10

Combine like terms: -24 + -10 = -34
12x = -34

Divide each side by '12'.
x = -2.833333333

Simplifying
x = -2.833333333

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