(6+w)(2+w)=252

Solution for (6+w)(2+w)=252 equation:

Simplifying
(6 + w)(2 + w) = 252

Multiply (6 + w) * (2 + w)
(6(2 + w) + w(2 + w)) = 252
((2 * 6 + w * 6) + w(2 + w)) = 252
((12 + 6w) + w(2 + w)) = 252
(12 + 6w + (2 * w + w * w)) = 252
(12 + 6w + (2w + w2)) = 252

Combine like terms: 6w + 2w = 8w
(12 + 8w + w2) = 252

Solving
12 + 8w + w2 = 252

Solving for variable 'w'.

Reorder the terms:
12 + -252 + 8w + w2 = 252 + -252

Combine like terms: 12 + -252 = -240
-240 + 8w + w2 = 252 + -252

Combine like terms: 252 + -252 = 0
-240 + 8w + w2 = 0

Factor a trinomial.
(-20 + -1w)(12 + -1w) = 0

Subproblem 1
Set the factor '(-20 + -1w)' equal to zero and attempt to solve:

Simplifying
-20 + -1w = 0

Solving
-20 + -1w = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1w = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1w = 0 + 20
-1w = 0 + 20

Combine like terms: 0 + 20 = 20
-1w = 20

Divide each side by '-1'.
w = -20

Simplifying
w = -20
Subproblem 2
Set the factor '(12 + -1w)' equal to zero and attempt to solve:

Simplifying
12 + -1w = 0

Solving
12 + -1w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1w = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1w = 0 + -12
-1w = 0 + -12

Combine like terms: 0 + -12 = -12
-1w = -12

Divide each side by '-1'.
w = 12

Simplifying
w = 12
Solution
w = {-20, 12}