t+12(3t-t^2)=

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

Simplifying
t + 12(3t + -1t2) = 0
t + (3t * 12 + -1t2 * 12) = 0
t + (36t + -12t2) = 0

Combine like terms: t + 36t = 37t
37t + -12t2 = 0

Solving
37t + -12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(37 + -12t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(37 + -12t)' equal to zero and attempt to solve:

Simplifying
37 + -12t = 0

Solving
37 + -12t = 0

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

Add '-37' to each side of the equation.
37 + -37 + -12t = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -12t = 0 + -37
-12t = 0 + -37

Combine like terms: 0 + -37 = -37
-12t = -37

Divide each side by '-12'.
t = 3.083333333

Simplifying
t = 3.083333333
Solution
t = {0, 3.083333333}