13t^2+40t+3=0

Solution for 13t^2+40t+3=0 equation:

Simplifying
13t2 + 40t + 3 = 0

Reorder the terms:
3 + 40t + 13t2 = 0

Solving
3 + 40t + 13t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + t)(1 + 13t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 13t)' equal to zero and attempt to solve:

Simplifying
1 + 13t = 0

Solving
1 + 13t = 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 + 13t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 13t = 0 + -1
13t = 0 + -1

Combine like terms: 0 + -1 = -1
13t = -1

Divide each side by '13'.
t = -0.07692307692

Simplifying
t = -0.07692307692
Solution
t = {-3, -0.07692307692}