(w+7)(w+2)=0

Solution for (w+7)(w+2)=0 equation:

Simplifying
(w + 7)(w + 2) = 0

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

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

Multiply (7 + w) * (2 + w)
(7(2 + w) + w(2 + w)) = 0
((2 * 7 + w * 7) + w(2 + w)) = 0
((14 + 7w) + w(2 + w)) = 0
(14 + 7w + (2 * w + w * w)) = 0
(14 + 7w + (2w + w2)) = 0

Combine like terms: 7w + 2w = 9w
(14 + 9w + w2) = 0

Solving
14 + 9w + w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve:

Simplifying
7 + w = 0

Solving
7 + w = 0

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

Add '-7' to each side of the equation.
7 + -7 + w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + w = 0 + -7
w = 0 + -7

Combine like terms: 0 + -7 = -7
w = -7

Simplifying
w = -7
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 = {-7, -2}