2a^2-8a-4=6

Solution for 2a^2-8a-4=6 equation:

Simplifying
2a2 + -8a + -4 = 6

Reorder the terms:
-4 + -8a + 2a2 = 6

Solving
-4 + -8a + 2a2 = 6

Solving for variable 'a'.

Reorder the terms:
-4 + -6 + -8a + 2a2 = 6 + -6

Combine like terms: -4 + -6 = -10
-10 + -8a + 2a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-10 + -8a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4a + a2) = 0

Factor a trinomial.
2((-1 + -1a)(5 + -1a)) = 0

Ignore the factor 2.
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 '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-1, 5}