2w^2-5w-2-w^2+8w-16=0

Solution for 2w^2-5w-2-w^2+8w-16=0 equation:

Simplifying
2w2 + -5w + -2 + -1w2 + 8w + -16 = 0

Reorder the terms:
-2 + -16 + -5w + 8w + 2w2 + -1w2 = 0

Combine like terms: -2 + -16 = -18
-18 + -5w + 8w + 2w2 + -1w2 = 0

Combine like terms: -5w + 8w = 3w
-18 + 3w + 2w2 + -1w2 = 0

Combine like terms: 2w2 + -1w2 = 1w2
-18 + 3w + 1w2 = 0

Solving
-18 + 3w + 1w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + -1w)(3 + -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 '(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
Solution
w = {-6, 3}