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

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Solution for (x+2)*(x+3)-(x-2)*(x+5)=6 equation: 


Simplifying
(x + 2)(x + 3) + -1(x + -2)(x + 5) = 6

Reorder the terms:
(2 + x)(x + 3) + -1(x + -2)(x + 5) = 6

Reorder the terms:
(2 + x)(3 + x) + -1(x + -2)(x + 5) = 6

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) + -1(x + -2)(x + 5) = 6
((3 * 2 + x * 2) + x(3 + x)) + -1(x + -2)(x + 5) = 6
((6 + 2x) + x(3 + x)) + -1(x + -2)(x + 5) = 6
(6 + 2x + (3 * x + x * x)) + -1(x + -2)(x + 5) = 6
(6 + 2x + (3x + x2)) + -1(x + -2)(x + 5) = 6

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) + -1(x + -2)(x + 5) = 6

Reorder the terms:
6 + 5x + x2 + -1(-2 + x)(x + 5) = 6

Reorder the terms:
6 + 5x + x2 + -1(-2 + x)(5 + x) = 6

Multiply (-2 + x) * (5 + x)
6 + 5x + x2 + -1(-2(5 + x) + x(5 + x)) = 6
6 + 5x + x2 + -1((5 * -2 + x * -2) + x(5 + x)) = 6
6 + 5x + x2 + -1((-10 + -2x) + x(5 + x)) = 6
6 + 5x + x2 + -1(-10 + -2x + (5 * x + x * x)) = 6
6 + 5x + x2 + -1(-10 + -2x + (5x + x2)) = 6

Combine like terms: -2x + 5x = 3x
6 + 5x + x2 + -1(-10 + 3x + x2) = 6
6 + 5x + x2 + (-10 * -1 + 3x * -1 + x2 * -1) = 6
6 + 5x + x2 + (10 + -3x + -1x2) = 6

Reorder the terms:
6 + 10 + 5x + -3x + x2 + -1x2 = 6

Combine like terms: 6 + 10 = 16
16 + 5x + -3x + x2 + -1x2 = 6

Combine like terms: 5x + -3x = 2x
16 + 2x + x2 + -1x2 = 6

Combine like terms: x2 + -1x2 = 0
16 + 2x + 0 = 6
16 + 2x = 6

Solving
16 + 2x = 6

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + 2x = 6 + -16

Combine like terms: 16 + -16 = 0
0 + 2x = 6 + -16
2x = 6 + -16

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

Divide each side by '2'.
x = -5

Simplifying
x = -5

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