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

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


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

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

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

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = (x + 5)(x + -2)
((3 * 2 + x * 2) + x(3 + x)) = (x + 5)(x + -2)
((6 + 2x) + x(3 + x)) = (x + 5)(x + -2)
(6 + 2x + (3 * x + x * x)) = (x + 5)(x + -2)
(6 + 2x + (3x + x2)) = (x + 5)(x + -2)

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = (x + 5)(x + -2)

Reorder the terms:
6 + 5x + x2 = (5 + x)(x + -2)

Reorder the terms:
6 + 5x + x2 = (5 + x)(-2 + x)

Multiply (5 + x) * (-2 + x)
6 + 5x + x2 = (5(-2 + x) + x(-2 + x))
6 + 5x + x2 = ((-2 * 5 + x * 5) + x(-2 + x))
6 + 5x + x2 = ((-10 + 5x) + x(-2 + x))
6 + 5x + x2 = (-10 + 5x + (-2 * x + x * x))
6 + 5x + x2 = (-10 + 5x + (-2x + x2))

Combine like terms: 5x + -2x = 3x
6 + 5x + x2 = (-10 + 3x + x2)

Add '-1x2' to each side of the equation.
6 + 5x + x2 + -1x2 = -10 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x + 0 = -10 + 3x + x2 + -1x2
6 + 5x = -10 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x = -10 + 3x + 0
6 + 5x = -10 + 3x

Solving
6 + 5x = -10 + 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
6 + 5x + -3x = -10 + 3x + -3x

Combine like terms: 5x + -3x = 2x
6 + 2x = -10 + 3x + -3x

Combine like terms: 3x + -3x = 0
6 + 2x = -10 + 0
6 + 2x = -10

Add '-6' to each side of the equation.
6 + -6 + 2x = -10 + -6

Combine like terms: 6 + -6 = 0
0 + 2x = -10 + -6
2x = -10 + -6

Combine like terms: -10 + -6 = -16
2x = -16

Divide each side by '2'.
x = -8

Simplifying
x = -8

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