(w+3)(w+2)=42

Solution for (w+3)(w+2)=42 equation:

Simplifying
(w + 3)(w + 2) = 42

Reorder the terms:
(3 + w)(w + 2) = 42

Reorder the terms:
(3 + w)(2 + w) = 42

Multiply (3 + w) * (2 + w)
(3(2 + w) + w(2 + w)) = 42
((2 * 3 + w * 3) + w(2 + w)) = 42
((6 + 3w) + w(2 + w)) = 42
(6 + 3w + (2 * w + w * w)) = 42
(6 + 3w + (2w + w2)) = 42

Combine like terms: 3w + 2w = 5w
(6 + 5w + w2) = 42

Solving
6 + 5w + w2 = 42

Solving for variable 'w'.

Reorder the terms:
6 + -42 + 5w + w2 = 42 + -42

Combine like terms: 6 + -42 = -36
-36 + 5w + w2 = 42 + -42

Combine like terms: 42 + -42 = 0
-36 + 5w + w2 = 0

Factor a trinomial.
(-9 + -1w)(4 + -1w) = 0

Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve:

Simplifying
-9 + -1w = 0

Solving
-9 + -1w = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1w = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1w = 0 + 9
-1w = 0 + 9

Combine like terms: 0 + 9 = 9
-1w = 9

Divide each side by '-1'.
w = -9

Simplifying
w = -9
Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-9, 4}