(x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0

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Solution for (x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0 equation: 


Simplifying
(x + 2)(x + 3) + (x + -3)(x + -2) + -2x(x + 1) = 0

Reorder the terms:
(2 + x)(x + 3) + (x + -3)(x + -2) + -2x(x + 1) = 0

Reorder the terms:
(2 + x)(3 + x) + (x + -3)(x + -2) + -2x(x + 1) = 0

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) + (x + -3)(x + -2) + -2x(x + 1) = 0
((3 * 2 + x * 2) + x(3 + x)) + (x + -3)(x + -2) + -2x(x + 1) = 0
((6 + 2x) + x(3 + x)) + (x + -3)(x + -2) + -2x(x + 1) = 0
(6 + 2x + (3 * x + x * x)) + (x + -3)(x + -2) + -2x(x + 1) = 0
(6 + 2x + (3x + x2)) + (x + -3)(x + -2) + -2x(x + 1) = 0

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) + (x + -3)(x + -2) + -2x(x + 1) = 0

Reorder the terms:
6 + 5x + x2 + (-3 + x)(x + -2) + -2x(x + 1) = 0

Reorder the terms:
6 + 5x + x2 + (-3 + x)(-2 + x) + -2x(x + 1) = 0

Multiply (-3 + x) * (-2 + x)
6 + 5x + x2 + (-3(-2 + x) + x(-2 + x)) + -2x(x + 1) = 0
6 + 5x + x2 + ((-2 * -3 + x * -3) + x(-2 + x)) + -2x(x + 1) = 0
6 + 5x + x2 + ((6 + -3x) + x(-2 + x)) + -2x(x + 1) = 0
6 + 5x + x2 + (6 + -3x + (-2 * x + x * x)) + -2x(x + 1) = 0
6 + 5x + x2 + (6 + -3x + (-2x + x2)) + -2x(x + 1) = 0

Combine like terms: -3x + -2x = -5x
6 + 5x + x2 + (6 + -5x + x2) + -2x(x + 1) = 0

Reorder the terms:
6 + 5x + x2 + 6 + -5x + x2 + -2x(1 + x) = 0
6 + 5x + x2 + 6 + -5x + x2 + (1 * -2x + x * -2x) = 0
6 + 5x + x2 + 6 + -5x + x2 + (-2x + -2x2) = 0

Reorder the terms:
6 + 6 + 5x + -5x + -2x + x2 + x2 + -2x2 = 0

Combine like terms: 6 + 6 = 12
12 + 5x + -5x + -2x + x2 + x2 + -2x2 = 0

Combine like terms: 5x + -5x = 0
12 + 0 + -2x + x2 + x2 + -2x2 = 0
12 + -2x + x2 + x2 + -2x2 = 0

Combine like terms: x2 + x2 = 2x2
12 + -2x + 2x2 + -2x2 = 0

Combine like terms: 2x2 + -2x2 = 0
12 + -2x + 0 = 0
12 + -2x = 0

Solving
12 + -2x = 0

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + -2x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -2x = 0 + -12
-2x = 0 + -12

Combine like terms: 0 + -12 = -12
-2x = -12

Divide each side by '-2'.
x = 6

Simplifying
x = 6

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