(w+4)(w+6)=8

Solution for (w+4)(w+6)=8 equation:

Simplifying
(w + 4)(w + 6) = 8

Reorder the terms:
(4 + w)(w + 6) = 8

Reorder the terms:
(4 + w)(6 + w) = 8

Multiply (4 + w) * (6 + w)
(4(6 + w) + w(6 + w)) = 8
((6 * 4 + w * 4) + w(6 + w)) = 8
((24 + 4w) + w(6 + w)) = 8
(24 + 4w + (6 * w + w * w)) = 8
(24 + 4w + (6w + w2)) = 8

Combine like terms: 4w + 6w = 10w
(24 + 10w + w2) = 8

Solving
24 + 10w + w2 = 8

Solving for variable 'w'.

Reorder the terms:
24 + -8 + 10w + w2 = 8 + -8

Combine like terms: 24 + -8 = 16
16 + 10w + w2 = 8 + -8

Combine like terms: 8 + -8 = 0
16 + 10w + w2 = 0

Factor a trinomial.
(8 + w)(2 + 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 '(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 = {-8, -2}