a^2-8a-84=0

Solution for a^2-8a-84=0 equation:

Simplifying
a2 + -8a + -84 = 0

Reorder the terms:
-84 + -8a + a2 = 0

Solving
-84 + -8a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -1a)(14 + -1a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(14 + -1a)' equal to zero and attempt to solve:

Simplifying
14 + -1a = 0

Solving
14 + -1a = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1a = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1a = 0 + -14
-1a = 0 + -14

Combine like terms: 0 + -14 = -14
-1a = -14

Divide each side by '-1'.
a = 14

Simplifying
a = 14
Solution
a = {-6, 14}