2(t-1)t=12

Solution for 2(t-1)t=12 equation:

Simplifying
2(t + -1) * t = 12

Reorder the terms:
2(-1 + t) * t = 12

Reorder the terms for easier multiplication:
2t(-1 + t) = 12
(-1 * 2t + t * 2t) = 12
(-2t + 2t2) = 12

Solving
-2t + 2t2 = 12

Solving for variable 't'.

Reorder the terms:
-12 + -2t + 2t2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -2t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1t + t2) = 0

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

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

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

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

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-2, 3}