24t^2+19t+2=0

Solution for 24t^2+19t+2=0 equation:

Simplifying
24t2 + 19t + 2 = 0

Reorder the terms:
2 + 19t + 24t2 = 0

Solving
2 + 19t + 24t2 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + 3t)(1 + 8t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 8t)' equal to zero and attempt to solve:

Simplifying
1 + 8t = 0

Solving
1 + 8t = 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 + 8t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8t = 0 + -1
8t = 0 + -1

Combine like terms: 0 + -1 = -1
8t = -1

Divide each side by '8'.
t = -0.125

Simplifying
t = -0.125
Solution
t = {-0.6666666667, -0.125}