a^2+6a-86=5

Solution for a^2+6a-86=5 equation:

Simplifying
a2 + 6a + -86 = 5

Reorder the terms:
-86 + 6a + a2 = 5

Solving
-86 + 6a + a2 = 5

Solving for variable 'a'.

Reorder the terms:
-86 + -5 + 6a + a2 = 5 + -5

Combine like terms: -86 + -5 = -91
-91 + 6a + a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-91 + 6a + a2 = 0

Factor a trinomial.
(-13 + -1a)(7 + -1a) = 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 '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-13, 7}