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

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

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

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

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

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

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

Solving
-6 + -1x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}