a=a^2-a-3

Solution for a=a^2-a-3 equation:

Simplifying
a = a2 + -1a + -3

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

Solving
a = -3 + -1a + a2

Solving for variable 'a'.

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

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

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

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

Combine like terms: -1a + a = 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}