3t^2+18t+t+6=0

Solution for 3t^2+18t+t+6=0 equation:

Simplifying
3t2 + 18t + t + 6 = 0

Reorder the terms:
6 + 18t + t + 3t2 = 0

Combine like terms: 18t + t = 19t
6 + 19t + 3t2 = 0

Solving
6 + 19t + 3t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 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 + t = 0 + -6

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

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

Simplifying
t = -6
Subproblem 2
Set the factor '(1 + 3t)' equal to zero and attempt to solve:

Simplifying
1 + 3t = 0

Solving
1 + 3t = 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 + 3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3t = 0 + -1
3t = 0 + -1

Combine like terms: 0 + -1 = -1
3t = -1

Divide each side by '3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Solution
t = {-6, -0.3333333333}