(w-8)(w+5)=14

Solution for (w-8)(w+5)=14 equation:

Simplifying
(w + -8)(w + 5) = 14

Reorder the terms:
(-8 + w)(w + 5) = 14

Reorder the terms:
(-8 + w)(5 + w) = 14

Multiply (-8 + w) * (5 + w)
(-8(5 + w) + w(5 + w)) = 14
((5 * -8 + w * -8) + w(5 + w)) = 14
((-40 + -8w) + w(5 + w)) = 14
(-40 + -8w + (5 * w + w * w)) = 14
(-40 + -8w + (5w + w2)) = 14

Combine like terms: -8w + 5w = -3w
(-40 + -3w + w2) = 14

Solving
-40 + -3w + w2 = 14

Solving for variable 'w'.

Reorder the terms:
-40 + -14 + -3w + w2 = 14 + -14

Combine like terms: -40 + -14 = -54
-54 + -3w + w2 = 14 + -14

Combine like terms: 14 + -14 = 0
-54 + -3w + w2 = 0

Factor a trinomial.
(-6 + -1w)(9 + -1w) = 0

Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve:

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1w = 0 + 6
-1w = 0 + 6

Combine like terms: 0 + 6 = 6
-1w = 6

Divide each side by '-1'.
w = -6

Simplifying
w = -6
Subproblem 2
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
Solution
w = {-6, 9}