a^2-1+a=5

Solution for a^2-1+a=5 equation:

Simplifying
a2 + -1 + a = 5

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

Solving
-1 + a + a2 = 5

Solving for variable 'a'.

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

Combine like terms: -1 + -5 = -6
-6 + a + a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-6 + a + a2 = 0

Factor a trinomial.
(-3 + -1a)(2 + -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 '(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
Solution
a = {-3, 2}