(3w-5)(2w)(w+7)=0

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Solution for (3w-5)(2w)(w+7)=0 equation: 


Simplifying
(3w + -5)(2w)(w + 7) = 0

Reorder the terms:
(-5 + 3w)(2w)(w + 7) = 0

Remove parenthesis around (2w)
(-5 + 3w) * 2w(w + 7) = 0

Reorder the terms:
(-5 + 3w) * 2w(7 + w) = 0

Reorder the terms for easier multiplication:
2w(-5 + 3w)(7 + w) = 0

Multiply (-5 + 3w) * (7 + w)
2w(-5(7 + w) + 3w * (7 + w)) = 0
2w((7 * -5 + w * -5) + 3w * (7 + w)) = 0
2w((-35 + -5w) + 3w * (7 + w)) = 0
2w(-35 + -5w + (7 * 3w + w * 3w)) = 0
2w(-35 + -5w + (21w + 3w2)) = 0

Combine like terms: -5w + 21w = 16w
2w(-35 + 16w + 3w2) = 0
(-35 * 2w + 16w * 2w + 3w2 * 2w) = 0
(-70w + 32w2 + 6w3) = 0

Solving
-70w + 32w2 + 6w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(-35 + 16w + 3w2) = 0

Factor a trinomial.
2w((-7 + -1w)(5 + -3w)) = 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 '(-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

Subproblem 3
Set the factor '(5 + -3w)' equal to zero and attempt to solve:

Simplifying
5 + -3w = 0

Solving
5 + -3w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3w = 0 + -5
-3w = 0 + -5

Combine like terms: 0 + -5 = -5
-3w = -5

Divide each side by '-3'.
w = 1.666666667

Simplifying
w = 1.666666667
Solution
w = {0, -7, 1.666666667}

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