32w^6+16w^5+48w^4=0

Solution for 32w^6+16w^5+48w^4=0 equation:

Simplifying
32w6 + 16w5 + 48w4 = 0

Reorder the terms:
48w4 + 16w5 + 32w6 = 0

Solving
48w4 + 16w5 + 32w6 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '16w4'.
16w4(3 + w + 2w2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor 'w4' equal to zero and attempt to solve:

Simplifying
w4 = 0

Solving
w4 = 0

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

Simplifying
w4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + w + 2w2)' equal to zero and attempt to solve:

Simplifying
3 + w + 2w2 = 0

Solving
3 + w + 2w2 = 0

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

Divide each side by '2'.
1.5 + 0.5w + w2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.5w + -1.5 + w2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.5w + w2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.5w + w2 = 0 + -1.5
0.5w + w2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.5w + w2 = -1.5

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5w + 0.25 + w2 = -1.5 + 0.25

Reorder the terms:
0.25 + 0.5w + w2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + 0.5w + w2 = -1.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = -1.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.