(w+2)(w+7)=6

Solution for (w+2)(w+7)=6 equation:

Simplifying
(w + 2)(w + 7) = 6

Reorder the terms:
(2 + w)(w + 7) = 6

Reorder the terms:
(2 + w)(7 + w) = 6

Multiply (2 + w) * (7 + w)
(2(7 + w) + w(7 + w)) = 6
((7 * 2 + w * 2) + w(7 + w)) = 6
((14 + 2w) + w(7 + w)) = 6
(14 + 2w + (7 * w + w * w)) = 6
(14 + 2w + (7w + w2)) = 6

Combine like terms: 2w + 7w = 9w
(14 + 9w + w2) = 6

Solving
14 + 9w + w2 = 6

Solving for variable 'w'.

Reorder the terms:
14 + -6 + 9w + w2 = 6 + -6

Combine like terms: 14 + -6 = 8
8 + 9w + w2 = 6 + -6

Combine like terms: 6 + -6 = 0
8 + 9w + w2 = 0

Factor a trinomial.
(8 + w)(1 + w) = 0

Subproblem 1
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + w = 0 + -8
w = 0 + -8

Combine like terms: 0 + -8 = -8
w = -8

Simplifying
w = -8
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 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 + w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + w = 0 + -1
w = 0 + -1

Combine like terms: 0 + -1 = -1
w = -1

Simplifying
w = -1
Solution
w = {-8, -1}