(4w+9)(8-w)=0

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Solution for (4w+9)(8-w)=0 equation: 


Simplifying
(4w + 9)(8 + -1w) = 0

Reorder the terms:
(9 + 4w)(8 + -1w) = 0

Multiply (9 + 4w) * (8 + -1w)
(9(8 + -1w) + 4w * (8 + -1w)) = 0
((8 * 9 + -1w * 9) + 4w * (8 + -1w)) = 0
((72 + -9w) + 4w * (8 + -1w)) = 0
(72 + -9w + (8 * 4w + -1w * 4w)) = 0
(72 + -9w + (32w + -4w2)) = 0

Combine like terms: -9w + 32w = 23w
(72 + 23w + -4w2) = 0

Solving
72 + 23w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(8 + -1w)(9 + 4w) = 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 + 4w)' equal to zero and attempt to solve:

Simplifying
9 + 4w = 0

Solving
9 + 4w = 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 + 4w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4w = 0 + -9
4w = 0 + -9

Combine like terms: 0 + -9 = -9
4w = -9

Divide each side by '4'.
w = -2.25

Simplifying
w = -2.25
Solution
w = {8, -2.25}

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