3t(t-1)=6

Solution for 3t(t-1)=6 equation:

Simplifying
3t(t + -1) = 6

Reorder the terms:
3t(-1 + t) = 6
(-1 * 3t + t * 3t) = 6
(-3t + 3t2) = 6

Solving
-3t + 3t2 = 6

Solving for variable 't'.

Reorder the terms:
-6 + -3t + 3t2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -3t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1t + t2) = 0

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

Ignore the factor 3.
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 + -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 = {-1, 2}