54t-12t^2=t

Solution for 54t-12t^2=t equation:

Simplifying
54t + -12t2 = t

Solving
54t + -12t2 = t

Solving for variable 't'.

Reorder the terms:
54t + -1t + -12t2 = t + -1t

Combine like terms: 54t + -1t = 53t
53t + -12t2 = t + -1t

Combine like terms: t + -1t = 0
53t + -12t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(53 + -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 '(53 + -12t)' equal to zero and attempt to solve:

Simplifying
53 + -12t = 0

Solving
53 + -12t = 0

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

Add '-53' to each side of the equation.
53 + -53 + -12t = 0 + -53

Combine like terms: 53 + -53 = 0
0 + -12t = 0 + -53
-12t = 0 + -53

Combine like terms: 0 + -53 = -53
-12t = -53

Divide each side by '-12'.
t = 4.416666667

Simplifying
t = 4.416666667
Solution
t = {0, 4.416666667}