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

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

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

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

Multiply (5 + 2w) * (2 + w)
(5(2 + w) + 2w * (2 + w)) = 0
((2 * 5 + w * 5) + 2w * (2 + w)) = 0
((10 + 5w) + 2w * (2 + w)) = 0
(10 + 5w + (2 * 2w + w * 2w)) = 0
(10 + 5w + (4w + 2w2)) = 0

Combine like terms: 5w + 4w = 9w
(10 + 9w + 2w2) = 0

Solving
10 + 9w + 2w2 = 0

Solving for variable 'w'.

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

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

Simplifying
5 + 2w = 0

Solving
5 + 2w = 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 + 2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2w = 0 + -5
2w = 0 + -5

Combine like terms: 0 + -5 = -5
2w = -5

Divide each side by '2'.
w = -2.5

Simplifying
w = -2.5
Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

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

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

Simplifying
w = -2
Solution
w = {-2.5, -2}