8c^2-2c-6=0

Solution for 8c^2-2c-6=0 equation:

Simplifying
8c2 + -2c + -6 = 0

Reorder the terms:
-6 + -2c + 8c2 = 0

Solving
-6 + -2c + 8c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1c + 4c2) = 0

Factor a trinomial.
2((-3 + -4c)(1 + -1c)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -4c)' equal to zero and attempt to solve:

Simplifying
-3 + -4c = 0

Solving
-3 + -4c = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4c = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4c = 0 + 3
-4c = 0 + 3

Combine like terms: 0 + 3 = 3
-4c = 3

Divide each side by '-4'.
c = -0.75

Simplifying
c = -0.75
Subproblem 2
Set the factor '(1 + -1c)' equal to zero and attempt to solve:

Simplifying
1 + -1c = 0

Solving
1 + -1c = 0

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

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

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

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

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

Simplifying
c = 1
Solution
c = {-0.75, 1}