6x^2y+60xy-30y=0

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Solution for 6x^2y+60xy-30y=0 equation: 


Simplifying
6x2y + 60xy + -30y = 0

Reorder the terms:
60xy + 6x2y + -30y = 0

Solving
60xy + 6x2y + -30y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6y'.
6y(10x + x2 + -5) = 0

Ignore the factor 6.

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

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

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 '(10x + x2 + -5)' equal to zero and attempt to solve:

Simplifying
10x + x2 + -5 = 0

Reorder the terms:
-5 + 10x + x2 = 0

Solving
-5 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 10x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 10x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 10x + x2 = 0 + 5
10x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
10x + x2 = 5

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 5 + 25

Reorder the terms:
25 + 10x + x2 = 5 + 25

Combine like terms: 5 + 25 = 30
25 + 10x + x2 = 30

Factor a perfect square on the left side:
(x + 5)(x + 5) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + 5) equal to 5.477225575 and -5.477225575.


Subproblem 1
x + 5 = 5.477225575

Simplifying
x + 5 = 5.477225575

Reorder the terms:
5 + x = 5.477225575

Solving
5 + x = 5.477225575

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 5.477225575 + -5

Combine like terms: 5 + -5 = 0
0 + x = 5.477225575 + -5
x = 5.477225575 + -5

Combine like terms: 5.477225575 + -5 = 0.477225575
x = 0.477225575

Simplifying
x = 0.477225575


Subproblem 2
x + 5 = -5.477225575

Simplifying
x + 5 = -5.477225575

Reorder the terms:
5 + x = -5.477225575

Solving
5 + x = -5.477225575

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -5.477225575 + -5

Combine like terms: 5 + -5 = 0
0 + x = -5.477225575 + -5
x = -5.477225575 + -5

Combine like terms: -5.477225575 + -5 = -10.477225575
x = -10.477225575

Simplifying
x = -10.477225575


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.477225575, -10.477225575}
Solution
x = {0.477225575, -10.477225575}

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