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

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


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

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

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