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

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

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

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

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

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

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

Solving
-6 + 1x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-3, 2}