(3w+7)(9-w)=0

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Solution for (3w+7)(9-w)=0 equation: 


Simplifying
(3w + 7)(9 + -1w) = 0

Reorder the terms:
(7 + 3w)(9 + -1w) = 0

Multiply (7 + 3w) * (9 + -1w)
(7(9 + -1w) + 3w * (9 + -1w)) = 0
((9 * 7 + -1w * 7) + 3w * (9 + -1w)) = 0
((63 + -7w) + 3w * (9 + -1w)) = 0
(63 + -7w + (9 * 3w + -1w * 3w)) = 0
(63 + -7w + (27w + -3w2)) = 0

Combine like terms: -7w + 27w = 20w
(63 + 20w + -3w2) = 0

Solving
63 + 20w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(9 + -1w)(7 + 3w) = 0


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

Simplifying
9 + -1w = 0

Solving
9 + -1w = 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 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9

Subproblem 2
Set the factor '(7 + 3w)' equal to zero and attempt to solve:

Simplifying
7 + 3w = 0

Solving
7 + 3w = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3w = 0 + -7
3w = 0 + -7

Combine like terms: 0 + -7 = -7
3w = -7

Divide each side by '3'.
w = -2.333333333

Simplifying
w = -2.333333333
Solution
w = {9, -2.333333333}

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