3w-5w*w=w(w-9)

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Solution for 3w-5w*w=w(w-9) equation: 


Simplifying
3w + -5w * w = w(w + -9)

Multiply w * w
3w + -5w2 = w(w + -9)

Reorder the terms:
3w + -5w2 = w(-9 + w)
3w + -5w2 = (-9 * w + w * w)
3w + -5w2 = (-9w + w2)

Solving
3w + -5w2 = -9w + w2

Solving for variable 'w'.

Reorder the terms:
3w + 9w + -5w2 + -1w2 = -9w + w2 + 9w + -1w2

Combine like terms: 3w + 9w = 12w
12w + -5w2 + -1w2 = -9w + w2 + 9w + -1w2

Combine like terms: -5w2 + -1w2 = -6w2
12w + -6w2 = -9w + w2 + 9w + -1w2

Reorder the terms:
12w + -6w2 = -9w + 9w + w2 + -1w2

Combine like terms: -9w + 9w = 0
12w + -6w2 = 0 + w2 + -1w2
12w + -6w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
12w + -6w2 = 0

Factor out the Greatest Common Factor (GCF), '6w'.
6w(2 + -1w) = 0

Ignore the factor 6.

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 '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

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

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {0, 2}

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