a^2-a-33=-3

Solution for a^2-a-33=-3 equation:

Simplifying
a2 + -1a + -33 = -3

Reorder the terms:
-33 + -1a + a2 = -3

Solving
-33 + -1a + a2 = -3

Solving for variable 'a'.

Reorder the terms:
-33 + 3 + -1a + a2 = -3 + 3

Combine like terms: -33 + 3 = -30
-30 + -1a + a2 = -3 + 3

Combine like terms: -3 + 3 = 0
-30 + -1a + a2 = 0

Factor a trinomial.
(-5 + -1a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-5, 6}