s^2=54-3s

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

Simplifying
s2 = 54 + -3s

Solving
s2 = 54 + -3s

Solving for variable 's'.

Reorder the terms:
-54 + 3s + s2 = 54 + -3s + -54 + 3s

Reorder the terms:
-54 + 3s + s2 = 54 + -54 + -3s + 3s

Combine like terms: 54 + -54 = 0
-54 + 3s + s2 = 0 + -3s + 3s
-54 + 3s + s2 = -3s + 3s

Combine like terms: -3s + 3s = 0
-54 + 3s + s2 = 0

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

Subproblem 1
Set the factor '(-9 + -1s)' equal to zero and attempt to solve:

Simplifying
-9 + -1s = 0

Solving
-9 + -1s = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1s = 0 + 9

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

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

Divide each side by '-1'.
s = -9

Simplifying
s = -9
Subproblem 2
Set the factor '(6 + -1s)' equal to zero and attempt to solve:

Simplifying
6 + -1s = 0

Solving
6 + -1s = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1s = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1s = 0 + -6
-1s = 0 + -6

Combine like terms: 0 + -6 = -6
-1s = -6

Divide each side by '-1'.
s = 6

Simplifying
s = 6
Solution
s = {-9, 6}