(w+2)(w+1)=12

Solution for (w+2)(w+1)=12 equation:

Simplifying
(w + 2)(w + 1) = 12

Reorder the terms:
(2 + w)(w + 1) = 12

Reorder the terms:
(2 + w)(1 + w) = 12

Multiply (2 + w) * (1 + w)
(2(1 + w) + w(1 + w)) = 12
((1 * 2 + w * 2) + w(1 + w)) = 12
((2 + 2w) + w(1 + w)) = 12
(2 + 2w + (1 * w + w * w)) = 12
(2 + 2w + (1w + w2)) = 12

Combine like terms: 2w + 1w = 3w
(2 + 3w + w2) = 12

Solving
2 + 3w + w2 = 12

Solving for variable 'w'.

Reorder the terms:
2 + -12 + 3w + w2 = 12 + -12

Combine like terms: 2 + -12 = -10
-10 + 3w + w2 = 12 + -12

Combine like terms: 12 + -12 = 0
-10 + 3w + w2 = 0

Factor a trinomial.
(-5 + -1w)(2 + -1w) = 0

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

Simplifying
-5 + -1w = 0

Solving
-5 + -1w = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1w = 0 + 5
-1w = 0 + 5

Combine like terms: 0 + 5 = 5
-1w = 5

Divide each side by '-1'.
w = -5

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-5, 2}