2w^3+10w^2=12w

Solution for 2w^3+10w^2=12w equation:

Simplifying
2w3 + 10w2 = 12w

Reorder the terms:
10w2 + 2w3 = 12w

Solving
10w2 + 2w3 = 12w

Solving for variable 'w'.

Reorder the terms:
-12w + 10w2 + 2w3 = 12w + -12w

Combine like terms: 12w + -12w = 0
-12w + 10w2 + 2w3 = 0

Factor out the Greatest Common Factor (GCF), '2w'.
2w(-6 + 5w + w2) = 0

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

Ignore the factor 2.
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 '(-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
Subproblem 3
Set the factor '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

Solving
1 + -1w = 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 + -1w = 0 + -1

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

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

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

Simplifying
w = 1
Solution
w = {0, -6, 1}