6t^2-5t-6=0

Solution for 6t^2-5t-6=0 equation:

Simplifying
6t2 + -5t + -6 = 0

Reorder the terms:
-6 + -5t + 6t2 = 0

Solving
-6 + -5t + 6t2 = 0

Solving for variable 't'.

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

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 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

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

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

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {-0.6666666667, 1.5}