13w^2+6w=-6w^3

Solution for 13w^2+6w=-6w^3 equation:

Simplifying
13w2 + 6w = -6w3

Reorder the terms:
6w + 13w2 = -6w3

Solving
6w + 13w2 = -6w3

Solving for variable 'w'.

Combine like terms: -6w3 + 6w3 = 0
6w + 13w2 + 6w3 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(6 + 13w + 6w2) = 0

Factor a trinomial.
w((3 + 2w)(2 + 3w)) = 0

Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

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

Simplifying
3 + 2w = 0

Solving
3 + 2w = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Subproblem 3
Set the factor '(2 + 3w)' equal to zero and attempt to solve:

Simplifying
2 + 3w = 0

Solving
2 + 3w = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3w = 0 + -2
3w = 0 + -2

Combine like terms: 0 + -2 = -2
3w = -2

Divide each side by '3'.
w = -0.6666666667

Simplifying
w = -0.6666666667
Solution
w = {0, -1.5, -0.6666666667}