(a-3)(a+2)=14

Solution for (a-3)(a+2)=14 equation:

Simplifying
(a + -3)(a + 2) = 14

Reorder the terms:
(-3 + a)(a + 2) = 14

Reorder the terms:
(-3 + a)(2 + a) = 14

Multiply (-3 + a) * (2 + a)
(-3(2 + a) + a(2 + a)) = 14
((2 * -3 + a * -3) + a(2 + a)) = 14
((-6 + -3a) + a(2 + a)) = 14
(-6 + -3a + (2 * a + a * a)) = 14
(-6 + -3a + (2a + a2)) = 14

Combine like terms: -3a + 2a = -1a
(-6 + -1a + a2) = 14

Solving
-6 + -1a + a2 = 14

Solving for variable 'a'.

Reorder the terms:
-6 + -14 + -1a + a2 = 14 + -14

Combine like terms: -6 + -14 = -20
-20 + -1a + a2 = 14 + -14

Combine like terms: 14 + -14 = 0
-20 + -1a + a2 = 0

Factor a trinomial.
(-4 + -1a)(5 + -1a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-4, 5}