3w(w-7)(w-1)=0

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Solution for 3w(w-7)(w-1)=0 equation: 


Simplifying
3w(w + -7)(w + -1) = 0

Reorder the terms:
3w(-7 + w)(w + -1) = 0

Reorder the terms:
3w(-7 + w)(-1 + w) = 0

Multiply (-7 + w) * (-1 + w)
3w(-7(-1 + w) + w(-1 + w)) = 0
3w((-1 * -7 + w * -7) + w(-1 + w)) = 0
3w((7 + -7w) + w(-1 + w)) = 0
3w(7 + -7w + (-1 * w + w * w)) = 0
3w(7 + -7w + (-1w + w2)) = 0

Combine like terms: -7w + -1w = -8w
3w(7 + -8w + w2) = 0
(7 * 3w + -8w * 3w + w2 * 3w) = 0
(21w + -24w2 + 3w3) = 0

Solving
21w + -24w2 + 3w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w'.
3w(7 + -8w + w2) = 0

Factor a trinomial.
3w((1 + -1w)(7 + -1w)) = 0

Ignore the factor 3.

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 + -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

Subproblem 3
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Solution
w = {0, 1, 7}

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