w(w+2)=w(10w-w)

Solution for w(w+2)=w(10w-w) equation:

Simplifying
w(w + 2) = w(10w + -1w)

Reorder the terms:
w(2 + w) = w(10w + -1w)
(2 * w + w * w) = w(10w + -1w)
(2w + w2) = w(10w + -1w)

Combine like terms: 10w + -1w = 9w
2w + w2 = w(9w)

Remove parenthesis around (9w)
2w + w2 = w * 9w

Reorder the terms for easier multiplication:
2w + w2 = 9w * w

Multiply w * w
2w + w2 = 9w2

Solving
2w + w2 = 9w2

Solving for variable 'w'.

Combine like terms: w2 + -9w2 = -8w2
2w + -8w2 = 9w2 + -9w2

Combine like terms: 9w2 + -9w2 = 0
2w + -8w2 = 0

Factor out the Greatest Common Factor (GCF), '2w'.
2w(1 + -4w) = 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 '(1 + -4w)' equal to zero and attempt to solve:

Simplifying
1 + -4w = 0

Solving
1 + -4w = 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 + -4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4w = 0 + -1
-4w = 0 + -1

Combine like terms: 0 + -1 = -1
-4w = -1

Divide each side by '-4'.
w = 0.25

Simplifying
w = 0.25
Solution
w = {0, 0.25}