(2a-2)=(a^2-5)

Solution for (2a-2)=(a^2-5) equation:

Simplifying
(2a + -2) = (a2 + -5)

Reorder the terms:
(-2 + 2a) = (a2 + -5)

Remove parenthesis around (-2 + 2a)
-2 + 2a = (a2 + -5)

Reorder the terms:
-2 + 2a = (-5 + a2)

Remove parenthesis around (-5 + a2)
-2 + 2a = -5 + a2

Solving
-2 + 2a = -5 + a2

Solving for variable 'a'.

Reorder the terms:
-2 + 5 + 2a + -1a2 = -5 + a2 + 5 + -1a2

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

Reorder the terms:
3 + 2a + -1a2 = -5 + 5 + a2 + -1a2

Combine like terms: -5 + 5 = 0
3 + 2a + -1a2 = 0 + a2 + -1a2
3 + 2a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
3 + 2a + -1a2 = 0

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

Simplifying
1 + a = 0

Solving
1 + a = 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 + a = 0 + -1

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

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

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