10w^4+45w^3+45w^2=0

Solution for 10w^4+45w^3+45w^2=0 equation:

Simplifying
10w4 + 45w3 + 45w2 = 0

Reorder the terms:
45w2 + 45w3 + 10w4 = 0

Solving
45w2 + 45w3 + 10w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w2'.
5w2(9 + 9w + 2w2) = 0

Factor a trinomial.
5w2((3 + w)(3 + 2w)) = 0

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

Simplifying
3 + w = 0

Solving
3 + w = 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 + w = 0 + -3

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

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

Simplifying
w = -3
Subproblem 3
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
Solution
w = {0, -3, -1.5}