=3t^2-6t+6

Solution for =3t^2-6t+6 equation:

Simplifying
0 = 3t2 + -6t + 6

Reorder the terms:
0 = 6 + -6t + 3t2

Solving
0 = 6 + -6t + 3t2

Solving for variable 't'.

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

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

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

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

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

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 2t + -1t2)' equal to zero and attempt to solve:

Simplifying
-2 + 2t + -1t2 = 0

Solving
-2 + 2t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2 + -2t + t2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + -2t + t2 = 0 + -2

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

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

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -2 + 1

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

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

Factor a perfect square on the left side:
(t + -1)(t + -1) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.