(8+w)(2w+9)=0

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Solution for (8+w)(2w+9)=0 equation: 


Simplifying
(8 + w)(2w + 9) = 0

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

Multiply (8 + w) * (9 + 2w)
(8(9 + 2w) + w(9 + 2w)) = 0
((9 * 8 + 2w * 8) + w(9 + 2w)) = 0
((72 + 16w) + w(9 + 2w)) = 0
(72 + 16w + (9 * w + 2w * w)) = 0
(72 + 16w + (9w + 2w2)) = 0

Combine like terms: 16w + 9w = 25w
(72 + 25w + 2w2) = 0

Solving
72 + 25w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(8 + w)(9 + 2w) = 0


Subproblem 1
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + w = 0 + -8
w = 0 + -8

Combine like terms: 0 + -8 = -8
w = -8

Simplifying
w = -8

Subproblem 2
Set the factor '(9 + 2w)' equal to zero and attempt to solve:

Simplifying
9 + 2w = 0

Solving
9 + 2w = 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 + 2w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2w = 0 + -9
2w = 0 + -9

Combine like terms: 0 + -9 = -9
2w = -9

Divide each side by '2'.
w = -4.5

Simplifying
w = -4.5
Solution
w = {-8, -4.5}

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