25x^2y+205xy-180y=0

Solution for 25x^2y+205xy-180y=0 equation:

Simplifying
25x2y + 205xy + -180y = 0

Reorder the terms:
205xy + 25x2y + -180y = 0

Solving
205xy + 25x2y + -180y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(41x + 5x2 + -36) = 0

Factor a trinomial.
5y((5x + -4)(x + 9)) = 0

Ignore the factor 5.
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 '(5x + -4)' equal to zero and attempt to solve:

Simplifying
5x + -4 = 0

Reorder the terms:
-4 + 5x = 0

Solving
-4 + 5x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 5x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5x = 0 + 4
5x = 0 + 4

Combine like terms: 0 + 4 = 4
5x = 4

Divide each side by '5'.
x = 0.8

Simplifying
x = 0.8
Subproblem 3
Set the factor '(x + 9)' equal to zero and attempt to solve:

Simplifying
x + 9 = 0

Reorder the terms:
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {0.8, -9}