4t^2-5t-6=0

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

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

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

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

Solving for variable 't'.

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

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

Simplifying
2 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-0.75, 2}