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

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

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

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

Multiply (1 + 2w) * (5 + w)
(1(5 + w) + 2w * (5 + w)) = 0
((5 * 1 + w * 1) + 2w * (5 + w)) = 0
((5 + 1w) + 2w * (5 + w)) = 0
(5 + 1w + (5 * 2w + w * 2w)) = 0
(5 + 1w + (10w + 2w2)) = 0

Combine like terms: 1w + 10w = 11w
(5 + 11w + 2w2) = 0

Solving
5 + 11w + 2w2 = 0

Solving for variable 'w'.

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

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 '(1 + 2w)' equal to zero and attempt to solve:

Simplifying
1 + 2w = 0

Solving
1 + 2w = 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 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Solution
w = {-5, -0.5}