(x-3)(x+2)=10-x

Solution for (x-3)(x+2)=10-x equation:

Simplifying
(x + -3)(x + 2) = 10 + -1x

Reorder the terms:
(-3 + x)(x + 2) = 10 + -1x

Reorder the terms:
(-3 + x)(2 + x) = 10 + -1x

Multiply (-3 + x) * (2 + x)
(-3(2 + x) + x(2 + x)) = 10 + -1x
((2 * -3 + x * -3) + x(2 + x)) = 10 + -1x
((-6 + -3x) + x(2 + x)) = 10 + -1x
(-6 + -3x + (2 * x + x * x)) = 10 + -1x
(-6 + -3x + (2x + x2)) = 10 + -1x

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

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

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

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

Solving
-6 + x2 = 10

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x2 = 10 + 6

Combine like terms: -6 + 6 = 0
0 + x2 = 10 + 6
x2 = 10 + 6

Combine like terms: 10 + 6 = 16
x2 = 16

Simplifying
x2 = 16

Take the square root of each side:
x = {-4, 4}