12x^3y-7x^2y-1xy=0

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Solution for 12x^3y-7x^2y-1xy=0 equation: 


Simplifying
12x3y + -7x2y + -1xy = 0

Reorder the terms:
-1xy + -7x2y + 12x3y = 0

Solving
-1xy + -7x2y + 12x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-1 + -7x + 12x2) = 0


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

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-1 + -7x + 12x2)' equal to zero and attempt to solve:

Simplifying
-1 + -7x + 12x2 = 0

Solving
-1 + -7x + 12x2 = 0

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
-0.08333333333 + -0.5833333333x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + -0.5833333333x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + -0.5833333333x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + -0.5833333333x + x2 = 0 + 0.08333333333
-0.5833333333x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
-0.5833333333x + x2 = 0.08333333333

The x term is -0.5833333333x.  Take half its coefficient (-0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
-0.5833333333x + 0.08506944446 + x2 = 0.08333333333 + 0.08506944446

Reorder the terms:
0.08506944446 + -0.5833333333x + x2 = 0.08333333333 + 0.08506944446

Combine like terms: 0.08333333333 + 0.08506944446 = 0.16840277779
0.08506944446 + -0.5833333333x + x2 = 0.16840277779

Factor a perfect square on the left side:
(x + -0.2916666667)(x + -0.2916666667) = 0.16840277779

Calculate the square root of the right side: 0.410369075

Break this problem into two subproblems by setting 
(x + -0.2916666667) equal to 0.410369075 and -0.410369075.


Subproblem 1
x + -0.2916666667 = 0.410369075

Simplifying
x + -0.2916666667 = 0.410369075

Reorder the terms:
-0.2916666667 + x = 0.410369075

Solving
-0.2916666667 + x = 0.410369075

Solving for variable 'x'.

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

Add '0.2916666667' to each side of the equation.
-0.2916666667 + 0.2916666667 + x = 0.410369075 + 0.2916666667

Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000
0.0000000000 + x = 0.410369075 + 0.2916666667
x = 0.410369075 + 0.2916666667

Combine like terms: 0.410369075 + 0.2916666667 = 0.7020357417
x = 0.7020357417

Simplifying
x = 0.7020357417


Subproblem 2
x + -0.2916666667 = -0.410369075

Simplifying
x + -0.2916666667 = -0.410369075

Reorder the terms:
-0.2916666667 + x = -0.410369075

Solving
-0.2916666667 + x = -0.410369075

Solving for variable 'x'.

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

Add '0.2916666667' to each side of the equation.
-0.2916666667 + 0.2916666667 + x = -0.410369075 + 0.2916666667

Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000
0.0000000000 + x = -0.410369075 + 0.2916666667
x = -0.410369075 + 0.2916666667

Combine like terms: -0.410369075 + 0.2916666667 = -0.1187024083
x = -0.1187024083

Simplifying
x = -0.1187024083


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7020357417, -0.1187024083}
Solution
x = {0.7020357417, -0.1187024083}

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