(5w+7)(9-w)=0

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Solution for (5w+7)(9-w)=0 equation: 


Simplifying
(5w + 7)(9 + -1w) = 0

Reorder the terms:
(7 + 5w)(9 + -1w) = 0

Multiply (7 + 5w) * (9 + -1w)
(7(9 + -1w) + 5w * (9 + -1w)) = 0
((9 * 7 + -1w * 7) + 5w * (9 + -1w)) = 0
((63 + -7w) + 5w * (9 + -1w)) = 0
(63 + -7w + (9 * 5w + -1w * 5w)) = 0
(63 + -7w + (45w + -5w2)) = 0

Combine like terms: -7w + 45w = 38w
(63 + 38w + -5w2) = 0

Solving
63 + 38w + -5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(9 + -1w)(7 + 5w) = 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 + 5w)' equal to zero and attempt to solve:

Simplifying
7 + 5w = 0

Solving
7 + 5w = 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 + 5w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5w = 0 + -7
5w = 0 + -7

Combine like terms: 0 + -7 = -7
5w = -7

Divide each side by '5'.
w = -1.4

Simplifying
w = -1.4
Solution
w = {9, -1.4}

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