8t^2+2t-6=0

Solution for 8t^2+2t-6=0 equation:

Simplifying
8t2 + 2t + -6 = 0

Reorder the terms:
-6 + 2t + 8t2 = 0

Solving
-6 + 2t + 8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + t + 4t2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve:

Simplifying
-1 + -1t = 0

Solving
-1 + -1t = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1t = 0 + 1

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

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

Divide each side by '-1'.
t = -1

Simplifying
t = -1
Subproblem 2
Set the factor '(3 + -4t)' equal to zero and attempt to solve:

Simplifying
3 + -4t = 0

Solving
3 + -4t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4t = 0 + -3

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

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

Divide each side by '-4'.
t = 0.75

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