(a+2)(a-3)=6

Solution for (a+2)(a-3)=6 equation:

Simplifying
(a + 2)(a + -3) = 6

Reorder the terms:
(2 + a)(a + -3) = 6

Reorder the terms:
(2 + a)(-3 + a) = 6

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

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

Solving
-6 + -1a + a2 = 6

Solving for variable 'a'.

Reorder the terms:
-6 + -6 + -1a + a2 = 6 + -6

Combine like terms: -6 + -6 = -12
-12 + -1a + a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-12 + -1a + a2 = 0

Factor a trinomial.
(-3 + -1a)(4 + -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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-3, 4}