3t^2=-12t+36

Solution for 3t^2=-12t+36 equation:

Simplifying
3t2 = -12t + 36

Reorder the terms:
3t2 = 36 + -12t

Solving
3t2 = 36 + -12t

Solving for variable 't'.

Reorder the terms:
-36 + 12t + 3t2 = 36 + -12t + -36 + 12t

Reorder the terms:
-36 + 12t + 3t2 = 36 + -36 + -12t + 12t

Combine like terms: 36 + -36 = 0
-36 + 12t + 3t2 = 0 + -12t + 12t
-36 + 12t + 3t2 = -12t + 12t

Combine like terms: -12t + 12t = 0
-36 + 12t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 4t + t2) = 0

Factor a trinomial.
3((-6 + -1t)(2 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
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 = {-6, 2}