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

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


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

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

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

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

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

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

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

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

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

Reorder the terms:
2 + -6 + -1x + -1x + -1x2 + x2 = 0

Combine like terms: 2 + -6 = -4
-4 + -1x + -1x + -1x2 + x2 = 0

Combine like terms: -1x + -1x = -2x
-4 + -2x + -1x2 + x2 = 0

Combine like terms: -1x2 + x2 = 0
-4 + -2x + 0 = 0
-4 + -2x = 0

Solving
-4 + -2x = 0

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + -2x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2x = 0 + 4
-2x = 0 + 4

Combine like terms: 0 + 4 = 4
-2x = 4

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

Simplifying
x = -2

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