w(x+y)2+7w(x+y)+12w=0

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Solution for w(x+y)2+7w(x+y)+12w=0 equation: 


Simplifying
w(x + y) * 2 + 7w(x + y) + 12w = 0

Reorder the terms for easier multiplication:
2w(x + y) + 7w(x + y) + 12w = 0
(x * 2w + y * 2w) + 7w(x + y) + 12w = 0
(2wx + 2wy) + 7w(x + y) + 12w = 0
2wx + 2wy + (x * 7w + y * 7w) + 12w = 0
2wx + 2wy + (7wx + 7wy) + 12w = 0

Reorder the terms:
12w + 2wx + 7wx + 2wy + 7wy = 0

Combine like terms: 2wx + 7wx = 9wx
12w + 9wx + 2wy + 7wy = 0

Combine like terms: 2wy + 7wy = 9wy
12w + 9wx + 9wy = 0

Solving
12w + 9wx + 9wy = 0

Solving for variable 'w'.

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

Factor out the Greatest Common Factor (GCF), '3w'.
3w(4 + 3x + 3y) = 0

Ignore the factor 3.

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 '(4 + 3x + 3y)' equal to zero and attempt to solve:

Simplifying
4 + 3x + 3y = 0

Solving
4 + 3x + 3y = 0

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

Add '-4' to each side of the equation.
4 + 3x + -4 + 3y = 0 + -4

Reorder the terms:
4 + -4 + 3x + 3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x + 3y = 0 + -4
3x + 3y = 0 + -4

Combine like terms: 0 + -4 = -4
3x + 3y = -4

Add '-3x' to each side of the equation.
3x + -3x + 3y = -4 + -3x

Combine like terms: 3x + -3x = 0
0 + 3y = -4 + -3x
3y = -4 + -3x

Add '-3y' to each side of the equation.
3y + -3y = -4 + -3x + -3y

Combine like terms: 3y + -3y = 0
0 = -4 + -3x + -3y

Simplifying
0 = -4 + -3x + -3y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
w = {0}

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