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

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

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

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

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

Combine like terms: 10w + 1w = 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}