t(3t+1)=2

Solution for t(3t+1)=2 equation:

Simplifying
t(3t + 1) = 2

Reorder the terms:
t(1 + 3t) = 2
(1 * t + 3t * t) = 2
(1t + 3t2) = 2

Solving
1t + 3t2 = 2

Solving for variable 't'.

Reorder the terms:
-2 + 1t + 3t2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 1t + 3t2 = 0

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

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

Simplifying
-1 + -1t = 0

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

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

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

Divide each side by '-1'.
t = -1

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

Simplifying
2 + -3t = 0

Solving
2 + -3t = 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 + -3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3t = 0 + -2
-3t = 0 + -2

Combine like terms: 0 + -2 = -2
-3t = -2

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Solution
t = {-1, 0.6666666667}