(a+4)(a-2)=-5

Solution for (a+4)(a-2)=-5 equation:

Simplifying
(a + 4)(a + -2) = -5

Reorder the terms:
(4 + a)(a + -2) = -5

Reorder the terms:
(4 + a)(-2 + a) = -5

Multiply (4 + a) * (-2 + a)
(4(-2 + a) + a(-2 + a)) = -5
((-2 * 4 + a * 4) + a(-2 + a)) = -5
((-8 + 4a) + a(-2 + a)) = -5
(-8 + 4a + (-2 * a + a * a)) = -5
(-8 + 4a + (-2a + a2)) = -5

Combine like terms: 4a + -2a = 2a
(-8 + 2a + a2) = -5

Solving
-8 + 2a + a2 = -5

Solving for variable 'a'.

Reorder the terms:
-8 + 5 + 2a + a2 = -5 + 5

Combine like terms: -8 + 5 = -3
-3 + 2a + a2 = -5 + 5

Combine like terms: -5 + 5 = 0
-3 + 2a + a2 = 0

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {-3, 1}