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

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

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

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

Multiply (2 + w) * (6 + 5w)
(2(6 + 5w) + w(6 + 5w)) = 0
((6 * 2 + 5w * 2) + w(6 + 5w)) = 0
((12 + 10w) + w(6 + 5w)) = 0
(12 + 10w + (6 * w + 5w * w)) = 0
(12 + 10w + (6w + 5w2)) = 0

Combine like terms: 10w + 6w = 16w
(12 + 16w + 5w2) = 0

Solving
12 + 16w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(2 + w)(6 + 5w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + 5w)' equal to zero and attempt to solve:

Simplifying
6 + 5w = 0

Solving
6 + 5w = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5w = 0 + -6
5w = 0 + -6

Combine like terms: 0 + -6 = -6
5w = -6

Divide each side by '5'.
w = -1.2

Simplifying
w = -1.2
Solution
w = {-2, -1.2}