-2(w+1)(-w+5)=0

Solution for -2(w+1)(-w+5)=0 equation:

Simplifying
-2(w + 1)(-1w + 5) = 0

Reorder the terms:
-2(1 + w)(-1w + 5) = 0

Reorder the terms:
-2(1 + w)(5 + -1w) = 0

Multiply (1 + w) * (5 + -1w)
-2(1(5 + -1w) + w(5 + -1w)) = 0
-2((5 * 1 + -1w * 1) + w(5 + -1w)) = 0
-2((5 + -1w) + w(5 + -1w)) = 0
-2(5 + -1w + (5 * w + -1w * w)) = 0
-2(5 + -1w + (5w + -1w2)) = 0

Combine like terms: -1w + 5w = 4w
-2(5 + 4w + -1w2) = 0
(5 * -2 + 4w * -2 + -1w2 * -2) = 0
(-10 + -8w + 2w2) = 0

Solving
-10 + -8w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4w + w2) = 0

Factor a trinomial.
2((-1 + -1w)(5 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-1, 5}