(w+7)(w+9)=80

Solution for (w+7)(w+9)=80 equation:

Simplifying
(w + 7)(w + 9) = 80

Reorder the terms:
(7 + w)(w + 9) = 80

Reorder the terms:
(7 + w)(9 + w) = 80

Multiply (7 + w) * (9 + w)
(7(9 + w) + w(9 + w)) = 80
((9 * 7 + w * 7) + w(9 + w)) = 80
((63 + 7w) + w(9 + w)) = 80
(63 + 7w + (9 * w + w * w)) = 80
(63 + 7w + (9w + w2)) = 80

Combine like terms: 7w + 9w = 16w
(63 + 16w + w2) = 80

Solving
63 + 16w + w2 = 80

Solving for variable 'w'.

Reorder the terms:
63 + -80 + 16w + w2 = 80 + -80

Combine like terms: 63 + -80 = -17
-17 + 16w + w2 = 80 + -80

Combine like terms: 80 + -80 = 0
-17 + 16w + w2 = 0

Factor a trinomial.
(-17 + -1w)(1 + -1w) = 0

Subproblem 1
Set the factor '(-17 + -1w)' equal to zero and attempt to solve:

Simplifying
-17 + -1w = 0

Solving
-17 + -1w = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1w = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1w = 0 + 17
-1w = 0 + 17

Combine like terms: 0 + 17 = 17
-1w = 17

Divide each side by '-1'.
w = -17

Simplifying
w = -17
Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1w = 0 + -1

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

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

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

Simplifying
w = 1
Solution
w = {-17, 1}