4w(w+2)(w-9)=0

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Solution for 4w(w+2)(w-9)=0 equation: 


Simplifying
4w(w + 2)(w + -9) = 0

Reorder the terms:
4w(2 + w)(w + -9) = 0

Reorder the terms:
4w(2 + w)(-9 + w) = 0

Multiply (2 + w) * (-9 + w)
4w(2(-9 + w) + w(-9 + w)) = 0
4w((-9 * 2 + w * 2) + w(-9 + w)) = 0
4w((-18 + 2w) + w(-9 + w)) = 0
4w(-18 + 2w + (-9 * w + w * w)) = 0
4w(-18 + 2w + (-9w + w2)) = 0

Combine like terms: 2w + -9w = -7w
4w(-18 + -7w + w2) = 0
(-18 * 4w + -7w * 4w + w2 * 4w) = 0
(-72w + -28w2 + 4w3) = 0

Solving
-72w + -28w2 + 4w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4w'.
4w(-18 + -7w + w2) = 0

Factor a trinomial.
4w((-2 + -1w)(9 + -1w)) = 0

Ignore the factor 4.

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

Subproblem 3
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {0, -2, 9}

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