25x^2y-43xy+6y=0

Solution for 25x^2y-43xy+6y=0 equation:

Simplifying
25x2y + -43xy + 6y = 0

Reorder the terms:
-43xy + 25x2y + 6y = 0

Solving
-43xy + 25x2y + 6y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-43x + 25x2 + 6) = 0

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 '(-43x + 25x2 + 6)' equal to zero and attempt to solve:

Simplifying
-43x + 25x2 + 6 = 0

Reorder the terms:
6 + -43x + 25x2 = 0

Solving
6 + -43x + 25x2 = 0

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

Divide each side by '25'.
0.24 + -1.72x + x2 = 0

Move the constant term to the right:

Add '-0.24' to each side of the equation.
0.24 + -1.72x + -0.24 + x2 = 0 + -0.24

Reorder the terms:
0.24 + -0.24 + -1.72x + x2 = 0 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
0.00 + -1.72x + x2 = 0 + -0.24
-1.72x + x2 = 0 + -0.24

Combine like terms: 0 + -0.24 = -0.24
-1.72x + x2 = -0.24

The x term is -1.72x.  Take half its coefficient (-0.86).
Square it (0.7396) and add it to both sides.

Add '0.7396' to each side of the equation.
-1.72x + 0.7396 + x2 = -0.24 + 0.7396

Reorder the terms:
0.7396 + -1.72x + x2 = -0.24 + 0.7396

Combine like terms: -0.24 + 0.7396 = 0.4996
0.7396 + -1.72x + x2 = 0.4996

Factor a perfect square on the left side:
(x + -0.86)(x + -0.86) = 0.4996

Calculate the square root of the right side: 0.706823882

Break this problem into two subproblems by setting 
(x + -0.86) equal to 0.706823882 and -0.706823882.

Subproblem 1
x + -0.86 = 0.706823882

Simplifying
x + -0.86 = 0.706823882

Reorder the terms:
-0.86 + x = 0.706823882

Solving
-0.86 + x = 0.706823882

Solving for variable 'x'.

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

Add '0.86' to each side of the equation.
-0.86 + 0.86 + x = 0.706823882 + 0.86

Combine like terms: -0.86 + 0.86 = 0.00
0.00 + x = 0.706823882 + 0.86
x = 0.706823882 + 0.86

Combine like terms: 0.706823882 + 0.86 = 1.566823882
x = 1.566823882

Simplifying
x = 1.566823882

Subproblem 2
x + -0.86 = -0.706823882

Simplifying
x + -0.86 = -0.706823882

Reorder the terms:
-0.86 + x = -0.706823882

Solving
-0.86 + x = -0.706823882

Solving for variable 'x'.

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

Add '0.86' to each side of the equation.
-0.86 + 0.86 + x = -0.706823882 + 0.86

Combine like terms: -0.86 + 0.86 = 0.00
0.00 + x = -0.706823882 + 0.86
x = -0.706823882 + 0.86

Combine like terms: -0.706823882 + 0.86 = 0.153176118
x = 0.153176118

Simplifying
x = 0.153176118

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.566823882, 0.153176118}
Solution
x = {1.566823882, 0.153176118}