5t^2+16t+12=0

Solution for 5t^2+16t+12=0 equation:

Simplifying
5t2 + 16t + 12 = 0

Reorder the terms:
12 + 16t + 5t2 = 0

Solving
12 + 16t + 5t2 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + t)(6 + 5t) = 0

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

Simplifying
2 + t = 0

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

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

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

Simplifying
t = -2
Subproblem 2
Set the factor '(6 + 5t)' equal to zero and attempt to solve:

Simplifying
6 + 5t = 0

Solving
6 + 5t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + 5t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5t = 0 + -6
5t = 0 + -6

Combine like terms: 0 + -6 = -6
5t = -6

Divide each side by '5'.
t = -1.2

Simplifying
t = -1.2
Solution
t = {-2, -1.2}