3t^2-13t-16=0

Solution for 3t^2-13t-16=0 equation:

Simplifying
3t2 + -13t + -16 = 0

Reorder the terms:
-16 + -13t + 3t2 = 0

Solving
-16 + -13t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -1t)(16 + -3t) = 0

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 '(16 + -3t)' equal to zero and attempt to solve:

Simplifying
16 + -3t = 0

Solving
16 + -3t = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3t = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3t = 0 + -16
-3t = 0 + -16

Combine like terms: 0 + -16 = -16
-3t = -16

Divide each side by '-3'.
t = 5.333333333

Simplifying
t = 5.333333333
Solution
t = {-1, 5.333333333}