(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 = 2w
(-63 + 2w + w2) = 80

Solving
-63 + 2w + w2 = 80

Solving for variable 'w'.

Reorder the terms:
-63 + -80 + 2w + w2 = 80 + -80

Combine like terms: -63 + -80 = -143
-143 + 2w + w2 = 80 + -80

Combine like terms: 80 + -80 = 0
-143 + 2w + w2 = 0

Factor a trinomial.
(-13 + -1w)(11 + -1w) = 0

Subproblem 1
Set the factor '(-13 + -1w)' equal to zero and attempt to solve:

Simplifying
-13 + -1w = 0

Solving
-13 + -1w = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1w = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1w = 0 + 13
-1w = 0 + 13

Combine like terms: 0 + 13 = 13
-1w = 13

Divide each side by '-1'.
w = -13

Simplifying
w = -13
Subproblem 2
Set the factor '(11 + -1w)' equal to zero and attempt to solve:

Simplifying
11 + -1w = 0

Solving
11 + -1w = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1w = 0 + -11
-1w = 0 + -11

Combine like terms: 0 + -11 = -11
-1w = -11

Divide each side by '-1'.
w = 11

Simplifying
w = 11
Solution
w = {-13, 11}