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

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

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

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

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

Multiply (-2 + a) * (3 + a)
(-2(3 + a) + a(3 + a)) = 0
((3 * -2 + a * -2) + a(3 + a)) = 0
((-6 + -2a) + a(3 + a)) = 0
(-6 + -2a + (3 * a + a * a)) = 0
(-6 + -2a + (3a + a2)) = 0

Combine like terms: -2a + 3a = 1a
(-6 + 1a + a2) = 0

Solving
-6 + 1a + a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

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

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

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

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

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

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

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