t^2=54-3t

Solution for t^2=54-3t equation:

Simplifying
t2 = 54 + -3t

Solving
t2 = 54 + -3t

Solving for variable 't'.

Reorder the terms:
-54 + 3t + t2 = 54 + -3t + -54 + 3t

Reorder the terms:
-54 + 3t + t2 = 54 + -54 + -3t + 3t

Combine like terms: 54 + -54 = 0
-54 + 3t + t2 = 0 + -3t + 3t
-54 + 3t + t2 = -3t + 3t

Combine like terms: -3t + 3t = 0
-54 + 3t + t2 = 0

Factor a trinomial.
(-9 + -1t)(6 + -1t) = 0

Subproblem 1
Set the factor '(-9 + -1t)' equal to zero and attempt to solve:

Simplifying
-9 + -1t = 0

Solving
-9 + -1t = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1t = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1t = 0 + 9
-1t = 0 + 9

Combine like terms: 0 + 9 = 9
-1t = 9

Divide each side by '-1'.
t = -9

Simplifying
t = -9
Subproblem 2
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
Solution
t = {-9, 6}