0=a^2-20a-96

Solution for 0=a^2-20a-96 equation:

Simplifying
0 = a2 + -20a + -96

Reorder the terms:
0 = -96 + -20a + a2

Solving
0 = -96 + -20a + a2

Solving for variable 'a'.

Combine like terms: 0 + 96 = 96
96 + 20a + -1a2 = -96 + -20a + a2 + 96 + 20a + -1a2

Reorder the terms:
96 + 20a + -1a2 = -96 + 96 + -20a + 20a + a2 + -1a2

Combine like terms: -96 + 96 = 0
96 + 20a + -1a2 = 0 + -20a + 20a + a2 + -1a2
96 + 20a + -1a2 = -20a + 20a + a2 + -1a2

Combine like terms: -20a + 20a = 0
96 + 20a + -1a2 = 0 + a2 + -1a2
96 + 20a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
96 + 20a + -1a2 = 0

Factor a trinomial.
(24 + -1a)(4 + a) = 0

Subproblem 1
Set the factor '(24 + -1a)' equal to zero and attempt to solve:

Simplifying
24 + -1a = 0

Solving
24 + -1a = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1a = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1a = 0 + -24
-1a = 0 + -24

Combine like terms: 0 + -24 = -24
-1a = -24

Divide each side by '-1'.
a = 24

Simplifying
a = 24
Subproblem 2
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

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

Add '-4' to each side of the equation.
4 + -4 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Solution
a = {24, -4}