-2(w-1)(-w-4)=0

Solution for -2(w-1)(-w-4)=0 equation:

Simplifying
-2(w + -1)(-1w + -4) = 0

Reorder the terms:
-2(-1 + w)(-1w + -4) = 0

Reorder the terms:
-2(-1 + w)(-4 + -1w) = 0

Multiply (-1 + w) * (-4 + -1w)
-2(-1(-4 + -1w) + w(-4 + -1w)) = 0
-2((-4 * -1 + -1w * -1) + w(-4 + -1w)) = 0
-2((4 + 1w) + w(-4 + -1w)) = 0
-2(4 + 1w + (-4 * w + -1w * w)) = 0
-2(4 + 1w + (-4w + -1w2)) = 0

Combine like terms: 1w + -4w = -3w
-2(4 + -3w + -1w2) = 0
(4 * -2 + -3w * -2 + -1w2 * -2) = 0
(-8 + 6w + 2w2) = 0

Solving
-8 + 6w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3w + w2) = 0

Factor a trinomial.
2((-4 + -1w)(1 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve:

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w = 0 + 4
-1w = 0 + 4

Combine like terms: 0 + 4 = 4
-1w = 4

Divide each side by '-1'.
w = -4

Simplifying
w = -4
Subproblem 2
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
Solution
w = {-4, 1}