6t^2-5t-4=0

Solution for 6t^2-5t-4=0 equation:

Simplifying
6t2 + -5t + -4 = 0

Reorder the terms:
-4 + -5t + 6t2 = 0

Solving
-4 + -5t + 6t2 = 0

Solving for variable 't'.

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

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

Simplifying
-1 + -2t = 0

Solving
-1 + -2t = 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 + -2t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2t = 0 + 1
-2t = 0 + 1

Combine like terms: 0 + 1 = 1
-2t = 1

Divide each side by '-2'.
t = -0.5

Simplifying
t = -0.5
Subproblem 2
Set the factor '(4 + -3t)' equal to zero and attempt to solve:

Simplifying
4 + -3t = 0

Solving
4 + -3t = 0

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

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

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

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

Divide each side by '-3'.
t = 1.333333333

Simplifying
t = 1.333333333
Solution
t = {-0.5, 1.333333333}