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

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


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

Reorder the terms for easier multiplication:
0 = x(12x + 6y)(x + y)

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

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

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

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

Reorder the terms:
0 = (6xy2 + 18x2y + 12x3)
0 = (6xy2 + 18x2y + 12x3)

Solving
0 = 6xy2 + 18x2y + 12x3

Solving for variable 'x'.
Remove the zero:
-6xy2 + -18x2y + -12x3 = 6xy2 + 18x2y + 12x3 + -6xy2 + -18x2y + -12x3

Reorder the terms:
-6xy2 + -18x2y + -12x3 = 6xy2 + -6xy2 + 18x2y + -18x2y + 12x3 + -12x3

Combine like terms: 6xy2 + -6xy2 = 0
-6xy2 + -18x2y + -12x3 = 0 + 18x2y + -18x2y + 12x3 + -12x3
-6xy2 + -18x2y + -12x3 = 18x2y + -18x2y + 12x3 + -12x3

Combine like terms: 18x2y + -18x2y = 0
-6xy2 + -18x2y + -12x3 = 0 + 12x3 + -12x3
-6xy2 + -18x2y + -12x3 = 12x3 + -12x3

Combine like terms: 12x3 + -12x3 = 0
-6xy2 + -18x2y + -12x3 = 0

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

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

Ignore the factor -6.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
y + x = 0

Reorder the terms:
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

Subproblem 3
Set the factor '(y + 2x)' equal to zero and attempt to solve:

Simplifying
y + 2x = 0

Reorder the terms:
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
Solution
x = {0, -1y, -0.5y}

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