6s^2=15+27s

Solution for 6s^2=15+27s equation:

Simplifying
6s2 = 15 + 27s

Solving
6s2 = 15 + 27s

Solving for variable 's'.

Reorder the terms:
-15 + -27s + 6s2 = 15 + 27s + -15 + -27s

Reorder the terms:
-15 + -27s + 6s2 = 15 + -15 + 27s + -27s

Combine like terms: 15 + -15 = 0
-15 + -27s + 6s2 = 0 + 27s + -27s
-15 + -27s + 6s2 = 27s + -27s

Combine like terms: 27s + -27s = 0
-15 + -27s + 6s2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -9s + 2s2) = 0

Factor a trinomial.
3((-1 + -2s)(5 + -1s)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -2s)' equal to zero and attempt to solve:

Simplifying
-1 + -2s = 0

Solving
-1 + -2s = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2s = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2s = 0 + 1
-2s = 0 + 1

Combine like terms: 0 + 1 = 1
-2s = 1

Divide each side by '-2'.
s = -0.5

Simplifying
s = -0.5
Subproblem 2
Set the factor '(5 + -1s)' equal to zero and attempt to solve:

Simplifying
5 + -1s = 0

Solving
5 + -1s = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1s = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1s = 0 + -5
-1s = 0 + -5

Combine like terms: 0 + -5 = -5
-1s = -5

Divide each side by '-1'.
s = 5

Simplifying
s = 5
Solution
s = {-0.5, 5}