(9-w)(2w+7)=0

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Solution for (9-w)(2w+7)=0 equation: 


Simplifying
(9 + -1w)(2w + 7) = 0

Reorder the terms:
(9 + -1w)(7 + 2w) = 0

Multiply (9 + -1w) * (7 + 2w)
(9(7 + 2w) + -1w * (7 + 2w)) = 0
((7 * 9 + 2w * 9) + -1w * (7 + 2w)) = 0
((63 + 18w) + -1w * (7 + 2w)) = 0
(63 + 18w + (7 * -1w + 2w * -1w)) = 0
(63 + 18w + (-7w + -2w2)) = 0

Combine like terms: 18w + -7w = 11w
(63 + 11w + -2w2) = 0

Solving
63 + 11w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(9 + -1w)(7 + 2w) = 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 + 2w)' equal to zero and attempt to solve:

Simplifying
7 + 2w = 0

Solving
7 + 2w = 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 + 2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2w = 0 + -7
2w = 0 + -7

Combine like terms: 0 + -7 = -7
2w = -7

Divide each side by '2'.
w = -3.5

Simplifying
w = -3.5
Solution
w = {9, -3.5}

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