(3t+1)(t-2)=

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

Simplifying
(3t + 1)(t + -2) = 0

Reorder the terms:
(1 + 3t)(t + -2) = 0

Reorder the terms:
(1 + 3t)(-2 + t) = 0

Multiply (1 + 3t) * (-2 + t)
(1(-2 + t) + 3t * (-2 + t)) = 0
((-2 * 1 + t * 1) + 3t * (-2 + t)) = 0
((-2 + 1t) + 3t * (-2 + t)) = 0
(-2 + 1t + (-2 * 3t + t * 3t)) = 0
(-2 + 1t + (-6t + 3t2)) = 0

Combine like terms: 1t + -6t = -5t
(-2 + -5t + 3t2) = 0

Solving
-2 + -5t + 3t2 = 0

Solving for variable 't'.

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

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-0.3333333333, 2}