20t^2+31t+12=0

Solution for 20t^2+31t+12=0 equation:

Simplifying
20t2 + 31t + 12 = 0

Reorder the terms:
12 + 31t + 20t2 = 0

Solving
12 + 31t + 20t2 = 0

Solving for variable 't'.

Factor a trinomial.
(4 + 5t)(3 + 4t) = 0

Subproblem 1
Set the factor '(4 + 5t)' equal to zero and attempt to solve:

Simplifying
4 + 5t = 0

Solving
4 + 5t = 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 + 5t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5t = 0 + -4
5t = 0 + -4

Combine like terms: 0 + -4 = -4
5t = -4

Divide each side by '5'.
t = -0.8

Simplifying
t = -0.8
Subproblem 2
Set the factor '(3 + 4t)' equal to zero and attempt to solve:

Simplifying
3 + 4t = 0

Solving
3 + 4t = 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 + 4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4t = 0 + -3
4t = 0 + -3

Combine like terms: 0 + -3 = -3
4t = -3

Divide each side by '4'.
t = -0.75

Simplifying
t = -0.75
Solution
t = {-0.8, -0.75}