a^2-7a-2=-8

Solution for a^2-7a-2=-8 equation:

Simplifying
a2 + -7a + -2 = -8

Reorder the terms:
-2 + -7a + a2 = -8

Solving
-2 + -7a + a2 = -8

Solving for variable 'a'.

Reorder the terms:
-2 + 8 + -7a + a2 = -8 + 8

Combine like terms: -2 + 8 = 6
6 + -7a + a2 = -8 + 8

Combine like terms: -8 + 8 = 0
6 + -7a + a2 = 0

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Subproblem 2
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
Solution
a = {1, 6}