3t^2+22t+32=0

Solution for 3t^2+22t+32=0 equation:

Simplifying
3t2 + 22t + 32 = 0

Reorder the terms:
32 + 22t + 3t2 = 0

Solving
32 + 22t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(16 + 3t)(2 + t) = 0

Subproblem 1
Set the factor '(16 + 3t)' equal to zero and attempt to solve:

Simplifying
16 + 3t = 0

Solving
16 + 3t = 0

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

Add '-16' to each side of the equation.
16 + -16 + 3t = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 3t = 0 + -16
3t = 0 + -16

Combine like terms: 0 + -16 = -16
3t = -16

Divide each side by '3'.
t = -5.333333333

Simplifying
t = -5.333333333
Subproblem 2
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
Solution
t = {-5.333333333, -2}