3t^2-12t=-12

Solution for 3t^2-12t=-12 equation:

Simplifying
3t2 + -12t = -12

Reorder the terms:
-12t + 3t2 = -12

Solving
-12t + 3t2 = -12

Solving for variable 't'.

Reorder the terms:
12 + -12t + 3t2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + -12t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -4t + t2) = 0

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

Ignore the factor 3.
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 '(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 = {2, 2}