w(w+7)(w-12)=0

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Solution for w(w+7)(w-12)=0 equation: 


Simplifying
w(w + 7)(w + -12) = 0

Reorder the terms:
w(7 + w)(w + -12) = 0

Reorder the terms:
w(7 + w)(-12 + w) = 0

Multiply (7 + w) * (-12 + w)
w(7(-12 + w) + w(-12 + w)) = 0
w((-12 * 7 + w * 7) + w(-12 + w)) = 0
w((-84 + 7w) + w(-12 + w)) = 0
w(-84 + 7w + (-12 * w + w * w)) = 0
w(-84 + 7w + (-12w + w2)) = 0

Combine like terms: 7w + -12w = -5w
w(-84 + -5w + w2) = 0
(-84 * w + -5w * w + w2 * w) = 0
(-84w + -5w2 + w3) = 0

Solving
-84w + -5w2 + w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w'.
w(-84 + -5w + w2) = 0

Factor a trinomial.
w((-7 + -1w)(12 + -1w)) = 0


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 '(12 + -1w)' equal to zero and attempt to solve:

Simplifying
12 + -1w = 0

Solving
12 + -1w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1w = 0 + -12

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

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

Divide each side by '-1'.
w = 12

Simplifying
w = 12
Solution
w = {0, -7, 12}

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