2t^2+13t=-21

Solution for 2t^2+13t=-21 equation:

Simplifying
2t2 + 13t = -21

Reorder the terms:
13t + 2t2 = -21

Solving
13t + 2t2 = -21

Solving for variable 't'.

Reorder the terms:
21 + 13t + 2t2 = -21 + 21

Combine like terms: -21 + 21 = 0
21 + 13t + 2t2 = 0

Factor a trinomial.
(7 + 2t)(3 + t) = 0

Subproblem 1
Set the factor '(7 + 2t)' equal to zero and attempt to solve:

Simplifying
7 + 2t = 0

Solving
7 + 2t = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2t = 0 + -7
2t = 0 + -7

Combine like terms: 0 + -7 = -7
2t = -7

Divide each side by '2'.
t = -3.5

Simplifying
t = -3.5
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

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

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

Simplifying
t = -3
Solution
t = {-3.5, -3}