5t^2+8t+3=0

Solution for 5t^2+8t+3=0 equation:

Simplifying
5t2 + 8t + 3 = 0

Reorder the terms:
3 + 8t + 5t2 = 0

Solving
3 + 8t + 5t2 = 0

Solving for variable 't'.

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

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

Simplifying
1 + t = 0

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

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

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

Simplifying
t = -1
Subproblem 2
Set the factor '(3 + 5t)' equal to zero and attempt to solve:

Simplifying
3 + 5t = 0

Solving
3 + 5t = 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 + 5t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5t = 0 + -3
5t = 0 + -3

Combine like terms: 0 + -3 = -3
5t = -3

Divide each side by '5'.
t = -0.6

Simplifying
t = -0.6
Solution
t = {-1, -0.6}