6t^2-14t-12=0

Solution for 6t^2-14t-12=0 equation:

Simplifying
6t2 + -14t + -12 = 0

Reorder the terms:
-12 + -14t + 6t2 = 0

Solving
-12 + -14t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -7t + 3t2) = 0

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

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

Simplifying
-2 + -3t = 0

Solving
-2 + -3t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3t = 0 + 2
-3t = 0 + 2

Combine like terms: 0 + 2 = 2
-3t = 2

Divide each side by '-3'.
t = -0.6666666667

Simplifying
t = -0.6666666667
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-0.6666666667, 3}