(w+6)(w+6)=3(w+12)-(w)(w)

Solution for (w+6)(w+6)=3(w+12)-(w)(w) equation:

Simplifying
(w + 6)(w + 6) = 3(w + 12) + -1(w)(w)

Reorder the terms:
(6 + w)(w + 6) = 3(w + 12) + -1(w)(w)

Reorder the terms:
(6 + w)(6 + w) = 3(w + 12) + -1(w)(w)

Multiply (6 + w) * (6 + w)
(6(6 + w) + w(6 + w)) = 3(w + 12) + -1(w)(w)
((6 * 6 + w * 6) + w(6 + w)) = 3(w + 12) + -1(w)(w)
((36 + 6w) + w(6 + w)) = 3(w + 12) + -1(w)(w)
(36 + 6w + (6 * w + w * w)) = 3(w + 12) + -1(w)(w)
(36 + 6w + (6w + w2)) = 3(w + 12) + -1(w)(w)

Combine like terms: 6w + 6w = 12w
(36 + 12w + w2) = 3(w + 12) + -1(w)(w)

Reorder the terms:
36 + 12w + w2 = 3(12 + w) + -1(w)(w)
36 + 12w + w2 = (12 * 3 + w * 3) + -1(w)(w)
36 + 12w + w2 = (36 + 3w) + -1(w)(w)

Multiply w * w
36 + 12w + w2 = 36 + 3w + -1w2

Add '-36' to each side of the equation.
36 + 12w + -36 + w2 = 36 + 3w + -36 + -1w2

Reorder the terms:
36 + -36 + 12w + w2 = 36 + 3w + -36 + -1w2

Combine like terms: 36 + -36 = 0
0 + 12w + w2 = 36 + 3w + -36 + -1w2
12w + w2 = 36 + 3w + -36 + -1w2

Reorder the terms:
12w + w2 = 36 + -36 + 3w + -1w2

Combine like terms: 36 + -36 = 0
12w + w2 = 0 + 3w + -1w2
12w + w2 = 3w + -1w2

Solving
12w + w2 = 3w + -1w2

Solving for variable 'w'.

Reorder the terms:
12w + -3w + w2 + w2 = 3w + -1w2 + -3w + w2

Combine like terms: 12w + -3w = 9w
9w + w2 + w2 = 3w + -1w2 + -3w + w2

Combine like terms: w2 + w2 = 2w2
9w + 2w2 = 3w + -1w2 + -3w + w2

Reorder the terms:
9w + 2w2 = 3w + -3w + -1w2 + w2

Combine like terms: 3w + -3w = 0
9w + 2w2 = 0 + -1w2 + w2
9w + 2w2 = -1w2 + w2

Combine like terms: -1w2 + w2 = 0
9w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(9 + 2w) = 0

Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
Set the factor '(9 + 2w)' equal to zero and attempt to solve:

Simplifying
9 + 2w = 0

Solving
9 + 2w = 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 + 2w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2w = 0 + -9
2w = 0 + -9

Combine like terms: 0 + -9 = -9
2w = -9

Divide each side by '2'.
w = -4.5

Simplifying
w = -4.5
Solution
w = {0, -4.5}