(x-3)(x+2)+(5-x)(x+1)=0

Solution for (x-3)(x+2)+(5-x)(x+1)=0 equation:

Simplifying
(x + -3)(x + 2) + (5 + -1x)(x + 1) = 0

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

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

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

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

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

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

Combine like terms: 5x + -1x = 4x
-6 + -1x + x2 + (5 + 4x + -1x2) = 0

Reorder the terms:
-6 + 5 + -1x + 4x + x2 + -1x2 = 0

Combine like terms: -6 + 5 = -1
-1 + -1x + 4x + x2 + -1x2 = 0

Combine like terms: -1x + 4x = 3x
-1 + 3x + x2 + -1x2 = 0

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

Solving
-1 + 3x = 0

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + 3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3x = 0 + 1
3x = 0 + 1

Combine like terms: 0 + 1 = 1
3x = 1

Divide each side by '3'.
x = 0.3333333333

Simplifying
x = 0.3333333333