3t^2-9t=12

Solution for 3t^2-9t=12 equation:

Simplifying
3t2 + -9t = 12

Reorder the terms:
-9t + 3t2 = 12

Solving
-9t + 3t2 = 12

Solving for variable 't'.

Reorder the terms:
-12 + -9t + 3t2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -9t + 3t2 = 0

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

Factor a trinomial.
3((-1 + -1t)(4 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-1, 4}