(3t-1)(t+5)=-13

Solution for (3t-1)(t+5)=-13 equation:

Simplifying
(3t + -1)(t + 5) = -13

Reorder the terms:
(-1 + 3t)(t + 5) = -13

Reorder the terms:
(-1 + 3t)(5 + t) = -13

Multiply (-1 + 3t) * (5 + t)
(-1(5 + t) + 3t * (5 + t)) = -13
((5 * -1 + t * -1) + 3t * (5 + t)) = -13
((-5 + -1t) + 3t * (5 + t)) = -13
(-5 + -1t + (5 * 3t + t * 3t)) = -13
(-5 + -1t + (15t + 3t2)) = -13

Combine like terms: -1t + 15t = 14t
(-5 + 14t + 3t2) = -13

Solving
-5 + 14t + 3t2 = -13

Solving for variable 't'.

Reorder the terms:
-5 + 13 + 14t + 3t2 = -13 + 13

Combine like terms: -5 + 13 = 8
8 + 14t + 3t2 = -13 + 13

Combine like terms: -13 + 13 = 0
8 + 14t + 3t2 = 0

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

Subproblem 1
Set the factor '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 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 + t = 0 + -4

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

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

Simplifying
t = -4
Subproblem 2
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
Solution
t = {-4, -0.6666666667}