(w-8)(w+6)=-33

Solution for (w-8)(w+6)=-33 equation:

Simplifying
(w + -8)(w + 6) = -33

Reorder the terms:
(-8 + w)(w + 6) = -33

Reorder the terms:
(-8 + w)(6 + w) = -33

Multiply (-8 + w) * (6 + w)
(-8(6 + w) + w(6 + w)) = -33
((6 * -8 + w * -8) + w(6 + w)) = -33
((-48 + -8w) + w(6 + w)) = -33
(-48 + -8w + (6 * w + w * w)) = -33
(-48 + -8w + (6w + w2)) = -33

Combine like terms: -8w + 6w = -2w
(-48 + -2w + w2) = -33

Solving
-48 + -2w + w2 = -33

Solving for variable 'w'.

Reorder the terms:
-48 + 33 + -2w + w2 = -33 + 33

Combine like terms: -48 + 33 = -15
-15 + -2w + w2 = -33 + 33

Combine like terms: -33 + 33 = 0
-15 + -2w + w2 = 0

Factor a trinomial.
(-3 + -1w)(5 + -1w) = 0

Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

Simplifying
w = -3
Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-3, 5}