4w^4-22w^3-12w^2=0

Solution for 4w^4-22w^3-12w^2=0 equation:

Simplifying
4w4 + -22w3 + -12w2 = 0

Reorder the terms:
-12w2 + -22w3 + 4w4 = 0

Solving
-12w2 + -22w3 + 4w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w2'.
2w2(-6 + -11w + 2w2) = 0

Factor a trinomial.
2w2((-1 + -2w)(6 + -1w)) = 0

Ignore the factor 2.
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 '(-1 + -2w)' equal to zero and attempt to solve:

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2w = 0 + 1
-2w = 0 + 1

Combine like terms: 0 + 1 = 1
-2w = 1

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 3
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {0, -0.5, 6}