(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 = 7w
(-72 + 7w + 2w2) = 0

Solving
-72 + 7w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-8 + -1w)(9 + -2w) = 0


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

Simplifying
-8 + -1w = 0

Solving
-8 + -1w = 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 + -1w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1w = 0 + 8
-1w = 0 + 8

Combine like terms: 0 + 8 = 8
-1w = 8

Divide each side by '-1'.
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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