=(12x+6y)(x+y)

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Solution for =(12x+6y)(x+y) equation: 


Simplifying
0 = (12x + 6y)(x + y)

Multiply (12x + 6y) * (x + y)
0 = (12x * (x + y) + 6y * (x + y))
0 = ((x * 12x + y * 12x) + 6y * (x + y))

Reorder the terms:
0 = ((12xy + 12x2) + 6y * (x + y))
0 = ((12xy + 12x2) + 6y * (x + y))
0 = (12xy + 12x2 + (x * 6y + y * 6y))
0 = (12xy + 12x2 + (6xy + 6y2))

Reorder the terms:
0 = (12xy + 6xy + 12x2 + 6y2)

Combine like terms: 12xy + 6xy = 18xy
0 = (18xy + 12x2 + 6y2)

Solving
0 = 18xy + 12x2 + 6y2

Solving for variable 'x'.
Remove the zero:
-18xy + -12x2 + -6y2 = 18xy + 12x2 + 6y2 + -18xy + -12x2 + -6y2

Reorder the terms:
-18xy + -12x2 + -6y2 = 18xy + -18xy + 12x2 + -12x2 + 6y2 + -6y2

Combine like terms: 18xy + -18xy = 0
-18xy + -12x2 + -6y2 = 0 + 12x2 + -12x2 + 6y2 + -6y2
-18xy + -12x2 + -6y2 = 12x2 + -12x2 + 6y2 + -6y2

Combine like terms: 12x2 + -12x2 = 0
-18xy + -12x2 + -6y2 = 0 + 6y2 + -6y2
-18xy + -12x2 + -6y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
-18xy + -12x2 + -6y2 = 0

Factor out the Greatest Common Factor (GCF), '-6'.
-6(3xy + 2x2 + y2) = 0

Factor a trinomial.
-6((2x + y)(x + y)) = 0

Ignore the factor -6.

Subproblem 1
Set the factor '(2x + y)' equal to zero and attempt to solve:

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y

Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y
Solution
x = {-0.5y, -1y}

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