8u^2-2u-6=0

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

Simplifying
8u2 + -2u + -6 = 0

Reorder the terms:
-6 + -2u + 8u2 = 0

Solving
-6 + -2u + 8u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1u + 4u2) = 0

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

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

Simplifying
-3 + -4u = 0

Solving
-3 + -4u = 0

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

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

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

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

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

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

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

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

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

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

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

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