(a-3)(a+1)=5

Solution for (a-3)(a+1)=5 equation:

Simplifying
(a + -3)(a + 1) = 5

Reorder the terms:
(-3 + a)(a + 1) = 5

Reorder the terms:
(-3 + a)(1 + a) = 5

Multiply (-3 + a) * (1 + a)
(-3(1 + a) + a(1 + a)) = 5
((1 * -3 + a * -3) + a(1 + a)) = 5
((-3 + -3a) + a(1 + a)) = 5
(-3 + -3a + (1 * a + a * a)) = 5
(-3 + -3a + (1a + a2)) = 5

Combine like terms: -3a + 1a = -2a
(-3 + -2a + a2) = 5

Solving
-3 + -2a + a2 = 5

Solving for variable 'a'.

Reorder the terms:
-3 + -5 + -2a + a2 = 5 + -5

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

Combine like terms: 5 + -5 = 0
-8 + -2a + a2 = 0

Factor a trinomial.
(-2 + -1a)(4 + -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 '(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 = {-2, 4}