t^2=27-6t

Solution for t^2=27-6t equation:

Simplifying
t2 = 27 + -6t

Solving
t2 = 27 + -6t

Solving for variable 't'.

Reorder the terms:
-27 + 6t + t2 = 27 + -6t + -27 + 6t

Reorder the terms:
-27 + 6t + t2 = 27 + -27 + -6t + 6t

Combine like terms: 27 + -27 = 0
-27 + 6t + t2 = 0 + -6t + 6t
-27 + 6t + t2 = -6t + 6t

Combine like terms: -6t + 6t = 0
-27 + 6t + t2 = 0

Factor a trinomial.
(-9 + -1t)(3 + -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 '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-9, 3}