9w^4-7w^3+8w^2=0

Solution for 9w^4-7w^3+8w^2=0 equation:

Simplifying
9w4 + -7w3 + 8w2 = 0

Reorder the terms:
8w2 + -7w3 + 9w4 = 0

Solving
8w2 + -7w3 + 9w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w2'.
w2(8 + -7w + 9w2) = 0

Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve:

Simplifying
w2 = 0

Solving
w2 = 0

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

Simplifying
w2 = 0

Take the square root of each side:
w = {0}
Subproblem 2
Set the factor '(8 + -7w + 9w2)' equal to zero and attempt to solve:

Simplifying
8 + -7w + 9w2 = 0

Solving
8 + -7w + 9w2 = 0

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

Divide each side by '9'.
0.8888888889 + -0.7777777778w + w2 = 0

Move the constant term to the right:

Add '-0.8888888889' to each side of the equation.
0.8888888889 + -0.7777777778w + -0.8888888889 + w2 = 0 + -0.8888888889

Reorder the terms:
0.8888888889 + -0.8888888889 + -0.7777777778w + w2 = 0 + -0.8888888889

Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000
0.0000000000 + -0.7777777778w + w2 = 0 + -0.8888888889
-0.7777777778w + w2 = 0 + -0.8888888889

Combine like terms: 0 + -0.8888888889 = -0.8888888889
-0.7777777778w + w2 = -0.8888888889

The w term is -0.7777777778w.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778w + 0.1512345679 + w2 = -0.8888888889 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778w + w2 = -0.8888888889 + 0.1512345679

Combine like terms: -0.8888888889 + 0.1512345679 = -0.737654321
0.1512345679 + -0.7777777778w + w2 = -0.737654321

Factor a perfect square on the left side:
(w + -0.3888888889)(w + -0.3888888889) = -0.737654321

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.
Solution
w = {0}