2x^3y+12x^2y-10xy=0

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Solution for 2x^3y+12x^2y-10xy=0 equation: 


Simplifying
2x3y + 12x2y + -10xy = 0

Reorder the terms:
-10xy + 12x2y + 2x3y = 0

Solving
-10xy + 12x2y + 2x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2xy'.
2xy(-5 + 6x + x2) = 0

Ignore the factor 2.

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 '(-5 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + 6x + x2 = 0

Solving
-5 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 6x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6x + x2 = 0 + 5
6x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
6x + x2 = 5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 5 + 9

Reorder the terms:
9 + 6x + x2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + 6x + x2 = 14

Factor a perfect square on the left side:
(x + 3)(x + 3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 3) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + 3 = 3.741657387

Simplifying
x + 3 = 3.741657387

Reorder the terms:
3 + x = 3.741657387

Solving
3 + x = 3.741657387

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.741657387 + -3
x = 3.741657387 + -3

Combine like terms: 3.741657387 + -3 = 0.741657387
x = 0.741657387

Simplifying
x = 0.741657387


Subproblem 2
x + 3 = -3.741657387

Simplifying
x + 3 = -3.741657387

Reorder the terms:
3 + x = -3.741657387

Solving
3 + x = -3.741657387

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.741657387 + -3
x = -3.741657387 + -3

Combine like terms: -3.741657387 + -3 = -6.741657387
x = -6.741657387

Simplifying
x = -6.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.741657387, -6.741657387}
Solution
x = {0.741657387, -6.741657387}

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