10s^3+36s^2+36s=18s

Solution for 10s^3+36s^2+36s=18s equation:

Simplifying
10s3 + 36s2 + 36s = 18s

Reorder the terms:
36s + 36s2 + 10s3 = 18s

Solving
36s + 36s2 + 10s3 = 18s

Solving for variable 's'.

Reorder the terms:
36s + -18s + 36s2 + 10s3 = 18s + -18s

Combine like terms: 36s + -18s = 18s
18s + 36s2 + 10s3 = 18s + -18s

Combine like terms: 18s + -18s = 0
18s + 36s2 + 10s3 = 0

Factor out the Greatest Common Factor (GCF), '2s'.
2s(9 + 18s + 5s2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor 's' equal to zero and attempt to solve:

Simplifying
s = 0

Solving
s = 0

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

Simplifying
s = 0
Subproblem 2
Set the factor '(3 + s)' equal to zero and attempt to solve:

Simplifying
3 + s = 0

Solving
3 + s = 0

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

Add '-3' to each side of the equation.
3 + -3 + s = 0 + -3

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

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

Simplifying
s = -3
Subproblem 3
Set the factor '(3 + 5s)' equal to zero and attempt to solve:

Simplifying
3 + 5s = 0

Solving
3 + 5s = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5s = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5s = 0 + -3
5s = 0 + -3

Combine like terms: 0 + -3 = -3
5s = -3

Divide each side by '5'.
s = -0.6

Simplifying
s = -0.6
Solution
s = {0, -3, -0.6}