(a+2)(a-3)=

Solution for (a+2)(a-3)= 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.
(-2 + -1a)(3 + -1a) = 0

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