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

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

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

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

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

Reorder the terms for easier multiplication:
2(4 + w)(1 + w) = 0

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

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

Solving
8 + 10w + 2w2 = 0

Solving for variable 'w'.

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

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

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

Simplifying
4 + w = 0

Solving
4 + w = 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 + w = 0 + -4

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

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

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

Simplifying
1 + w = 0

Solving
1 + w = 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 + w = 0 + -1

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

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

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