(a+3)(a-2)=36

Solution for (a+3)(a-2)=36 equation:

Simplifying
(a + 3)(a + -2) = 36

Reorder the terms:
(3 + a)(a + -2) = 36

Reorder the terms:
(3 + a)(-2 + a) = 36

Multiply (3 + a) * (-2 + a)
(3(-2 + a) + a(-2 + a)) = 36
((-2 * 3 + a * 3) + a(-2 + a)) = 36
((-6 + 3a) + a(-2 + a)) = 36
(-6 + 3a + (-2 * a + a * a)) = 36
(-6 + 3a + (-2a + a2)) = 36

Combine like terms: 3a + -2a = 1a
(-6 + 1a + a2) = 36

Solving
-6 + 1a + a2 = 36

Solving for variable 'a'.

Reorder the terms:
-6 + -36 + 1a + a2 = 36 + -36

Combine like terms: -6 + -36 = -42
-42 + 1a + a2 = 36 + -36

Combine like terms: 36 + -36 = 0
-42 + 1a + a2 = 0

Factor a trinomial.
(-7 + -1a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve:

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

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

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

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-7, 6}