s^3+s^2=42s

Solution for s^3+s^2=42s equation:

Simplifying
s3 + s2 = 42s

Reorder the terms:
s2 + s3 = 42s

Solving
s2 + s3 = 42s

Solving for variable 's'.

Reorder the terms:
-42s + s2 + s3 = 42s + -42s

Combine like terms: 42s + -42s = 0
-42s + s2 + s3 = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-42 + s + s2) = 0

Factor a trinomial.
s((-7 + -1s)(6 + -1s)) = 0

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 '(-7 + -1s)' equal to zero and attempt to solve:

Simplifying
-7 + -1s = 0

Solving
-7 + -1s = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1s = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1s = 0 + 7
-1s = 0 + 7

Combine like terms: 0 + 7 = 7
-1s = 7

Divide each side by '-1'.
s = -7

Simplifying
s = -7
Subproblem 3
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 = {0, -7, 6}