(w+4)(w+5)=12

Solution for (w+4)(w+5)=12 equation:

Simplifying
(w + 4)(w + 5) = 12

Reorder the terms:
(4 + w)(w + 5) = 12

Reorder the terms:
(4 + w)(5 + w) = 12

Multiply (4 + w) * (5 + w)
(4(5 + w) + w(5 + w)) = 12
((5 * 4 + w * 4) + w(5 + w)) = 12
((20 + 4w) + w(5 + w)) = 12
(20 + 4w + (5 * w + w * w)) = 12
(20 + 4w + (5w + w2)) = 12

Combine like terms: 4w + 5w = 9w
(20 + 9w + w2) = 12

Solving
20 + 9w + w2 = 12

Solving for variable 'w'.

Reorder the terms:
20 + -12 + 9w + w2 = 12 + -12

Combine like terms: 20 + -12 = 8
8 + 9w + w2 = 12 + -12

Combine like terms: 12 + -12 = 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}