(3w-8)(9-w)=0

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Solution for (3w-8)(9-w)=0 equation: 


Simplifying
(3w + -8)(9 + -1w) = 0

Reorder the terms:
(-8 + 3w)(9 + -1w) = 0

Multiply (-8 + 3w) * (9 + -1w)
(-8(9 + -1w) + 3w * (9 + -1w)) = 0
((9 * -8 + -1w * -8) + 3w * (9 + -1w)) = 0
((-72 + 8w) + 3w * (9 + -1w)) = 0
(-72 + 8w + (9 * 3w + -1w * 3w)) = 0
(-72 + 8w + (27w + -3w2)) = 0

Combine like terms: 8w + 27w = 35w
(-72 + 35w + -3w2) = 0

Solving
-72 + 35w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + w)(8 + -3w) = 0


Subproblem 1
Set the factor '(-9 + w)' equal to zero and attempt to solve:

Simplifying
-9 + w = 0

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

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

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

Simplifying
w = 9

Subproblem 2
Set the factor '(8 + -3w)' equal to zero and attempt to solve:

Simplifying
8 + -3w = 0

Solving
8 + -3w = 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 + -3w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3w = 0 + -8
-3w = 0 + -8

Combine like terms: 0 + -8 = -8
-3w = -8

Divide each side by '-3'.
w = 2.666666667

Simplifying
w = 2.666666667
Solution
w = {9, 2.666666667}

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