3t^2-10t-13=0

Solution for 3t^2-10t-13=0 equation:

Simplifying
3t2 + -10t + -13 = 0

Reorder the terms:
-13 + -10t + 3t2 = 0

Solving
-13 + -10t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -1t)(13 + -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 '(13 + -3t)' equal to zero and attempt to solve:

Simplifying
13 + -3t = 0

Solving
13 + -3t = 0

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

Add '-13' to each side of the equation.
13 + -13 + -3t = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -3t = 0 + -13
-3t = 0 + -13

Combine like terms: 0 + -13 = -13
-3t = -13

Divide each side by '-3'.
t = 4.333333333

Simplifying
t = 4.333333333
Solution
t = {-1, 4.333333333}