8t^2+10t+3=0

Solution for 8t^2+10t+3=0 equation:

Simplifying
8t2 + 10t + 3 = 0

Reorder the terms:
3 + 10t + 8t2 = 0

Solving
3 + 10t + 8t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + 4t)(1 + 2t) = 0

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

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {-0.75, -0.5}