(2w+6)(w+5)=0

Solution for (2w+6)(w+5)=0 equation:

Simplifying
(2w + 6)(w + 5) = 0

Reorder the terms:
(6 + 2w)(w + 5) = 0

Reorder the terms:
(6 + 2w)(5 + w) = 0

Multiply (6 + 2w) * (5 + w)
(6(5 + w) + 2w * (5 + w)) = 0
((5 * 6 + w * 6) + 2w * (5 + w)) = 0
((30 + 6w) + 2w * (5 + w)) = 0
(30 + 6w + (5 * 2w + w * 2w)) = 0
(30 + 6w + (10w + 2w2)) = 0

Combine like terms: 6w + 10w = 16w
(30 + 16w + 2w2) = 0

Solving
30 + 16w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 8w + w2) = 0

Factor a trinomial.
2((5 + w)(3 + w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 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 + w = 0 + -5

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

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

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

Simplifying
3 + w = 0

Solving
3 + w = 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 + w = 0 + -3

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

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

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