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

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

Simplifying
3t = 3(t2 + -2t + 2)

Reorder the terms:
3t = 3(2 + -2t + t2)
3t = (2 * 3 + -2t * 3 + t2 * 3)
3t = (6 + -6t + 3t2)

Solving
3t = 6 + -6t + 3t2

Solving for variable 't'.

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

Combine like terms: 3t + 6t = 9t
-6 + 9t + -3t2 = 6 + -6t + 3t2 + -6 + 6t + -3t2

Reorder the terms:
-6 + 9t + -3t2 = 6 + -6 + -6t + 6t + 3t2 + -3t2

Combine like terms: 6 + -6 = 0
-6 + 9t + -3t2 = 0 + -6t + 6t + 3t2 + -3t2
-6 + 9t + -3t2 = -6t + 6t + 3t2 + -3t2

Combine like terms: -6t + 6t = 0
-6 + 9t + -3t2 = 0 + 3t2 + -3t2
-6 + 9t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-6 + 9t + -3t2 = 0

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

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

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

Simplifying
-2 + t = 0

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

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

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

Simplifying
t = 2
Subproblem 2
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
Solution
t = {2, 1}