(w+2)(5w+15)=0

Solution for (w+2)(5w+15)=0 equation:

Simplifying
(w + 2)(5w + 15) = 0

Reorder the terms:
(2 + w)(5w + 15) = 0

Reorder the terms:
(2 + w)(15 + 5w) = 0

Multiply (2 + w) * (15 + 5w)
(2(15 + 5w) + w(15 + 5w)) = 0
((15 * 2 + 5w * 2) + w(15 + 5w)) = 0
((30 + 10w) + w(15 + 5w)) = 0
(30 + 10w + (15 * w + 5w * w)) = 0
(30 + 10w + (15w + 5w2)) = 0

Combine like terms: 10w + 15w = 25w
(30 + 25w + 5w2) = 0

Solving
30 + 25w + 5w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + 5w + w2) = 0

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

Ignore the factor 5.
Subproblem 1
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
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 = {-3, -2}