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

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


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

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

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

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

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

Solving
-72 + 28w + 4w2 = 0

Solving for variable 'w'.

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

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

Ignore the factor 4.

Subproblem 1
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

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 = {-9, 2}

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