15w^3-48w^2+9w=3w

Solution for 15w^3-48w^2+9w=3w equation:

Simplifying
15w3 + -48w2 + 9w = 3w

Reorder the terms:
9w + -48w2 + 15w3 = 3w

Solving
9w + -48w2 + 15w3 = 3w

Solving for variable 'w'.

Reorder the terms:
9w + -3w + -48w2 + 15w3 = 3w + -3w

Combine like terms: 9w + -3w = 6w
6w + -48w2 + 15w3 = 3w + -3w

Combine like terms: 3w + -3w = 0
6w + -48w2 + 15w3 = 0

Factor out the Greatest Common Factor (GCF), '3w'.
3w(2 + -16w + 5w2) = 0

Ignore the factor 3.
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 '(2 + -16w + 5w2)' equal to zero and attempt to solve:

Simplifying
2 + -16w + 5w2 = 0

Solving
2 + -16w + 5w2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.4 + -3.2w + w2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -3.2w + -0.4 + w2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -3.2w + w2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -3.2w + w2 = 0 + -0.4
-3.2w + w2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-3.2w + w2 = -0.4

The w term is -3.2w.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2w + 2.56 + w2 = -0.4 + 2.56

Reorder the terms:
2.56 + -3.2w + w2 = -0.4 + 2.56

Combine like terms: -0.4 + 2.56 = 2.16
2.56 + -3.2w + w2 = 2.16

Factor a perfect square on the left side:
(w + -1.6)(w + -1.6) = 2.16

Calculate the square root of the right side: 1.469693846

Break this problem into two subproblems by setting 
(w + -1.6) equal to 1.469693846 and -1.469693846.

Subproblem 1
w + -1.6 = 1.469693846

Simplifying
w + -1.6 = 1.469693846

Reorder the terms:
-1.6 + w = 1.469693846

Solving
-1.6 + w = 1.469693846

Solving for variable 'w'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + w = 1.469693846 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + w = 1.469693846 + 1.6
w = 1.469693846 + 1.6

Combine like terms: 1.469693846 + 1.6 = 3.069693846
w = 3.069693846

Simplifying
w = 3.069693846

Subproblem 2
w + -1.6 = -1.469693846

Simplifying
w + -1.6 = -1.469693846

Reorder the terms:
-1.6 + w = -1.469693846

Solving
-1.6 + w = -1.469693846

Solving for variable 'w'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + w = -1.469693846 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + w = -1.469693846 + 1.6
w = -1.469693846 + 1.6

Combine like terms: -1.469693846 + 1.6 = 0.130306154
w = 0.130306154

Simplifying
w = 0.130306154

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.069693846, 0.130306154}
Solution
w = {0, 3.069693846, 0.130306154}