0=a^2-8a-33

Solution for 0=a^2-8a-33 equation:

Simplifying
0 = a2 + -8a + -33

Reorder the terms:
0 = -33 + -8a + a2

Solving
0 = -33 + -8a + a2

Solving for variable 'a'.

Combine like terms: 0 + 33 = 33
33 + 8a + -1a2 = -33 + -8a + a2 + 33 + 8a + -1a2

Reorder the terms:
33 + 8a + -1a2 = -33 + 33 + -8a + 8a + a2 + -1a2

Combine like terms: -33 + 33 = 0
33 + 8a + -1a2 = 0 + -8a + 8a + a2 + -1a2
33 + 8a + -1a2 = -8a + 8a + a2 + -1a2

Combine like terms: -8a + 8a = 0
33 + 8a + -1a2 = 0 + a2 + -1a2
33 + 8a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
33 + 8a + -1a2 = 0

Factor a trinomial.
(11 + -1a)(3 + a) = 0

Subproblem 1
Set the factor '(11 + -1a)' equal to zero and attempt to solve:

Simplifying
11 + -1a = 0

Solving
11 + -1a = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1a = 0 + -11
-1a = 0 + -11

Combine like terms: 0 + -11 = -11
-1a = -11

Divide each side by '-1'.
a = 11

Simplifying
a = 11
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Solution
a = {11, -3}