=a^2-4a-117

Solution for =a^2-4a-117 equation:

Simplifying
0 = a2 + -4a + -117

Reorder the terms:
0 = -117 + -4a + a2

Solving
0 = -117 + -4a + a2

Solving for variable 'a'.

Combine like terms: 0 + 117 = 117
117 + 4a + -1a2 = -117 + -4a + a2 + 117 + 4a + -1a2

Reorder the terms:
117 + 4a + -1a2 = -117 + 117 + -4a + 4a + a2 + -1a2

Combine like terms: -117 + 117 = 0
117 + 4a + -1a2 = 0 + -4a + 4a + a2 + -1a2
117 + 4a + -1a2 = -4a + 4a + a2 + -1a2

Combine like terms: -4a + 4a = 0
117 + 4a + -1a2 = 0 + a2 + -1a2
117 + 4a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
117 + 4a + -1a2 = 0

Factor a trinomial.
(13 + -1a)(9 + a) = 0

Subproblem 1
Set the factor '(13 + -1a)' equal to zero and attempt to solve:

Simplifying
13 + -1a = 0

Solving
13 + -1a = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1a = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1a = 0 + -13
-1a = 0 + -13

Combine like terms: 0 + -13 = -13
-1a = -13

Divide each side by '-1'.
a = 13

Simplifying
a = 13
Subproblem 2
Set the factor '(9 + a)' equal to zero and attempt to solve:

Simplifying
9 + a = 0

Solving
9 + a = 0

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

Add '-9' to each side of the equation.
9 + -9 + a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + a = 0 + -9
a = 0 + -9

Combine like terms: 0 + -9 = -9
a = -9

Simplifying
a = -9
Solution
a = {13, -9}