4y^2=xy-6y

Solution for 4y^2=xy-6y equation:

Simplifying
4y2 = xy + -6y

Solving
4y2 = xy + -6y

Solving for variable 'y'.

Reorder the terms:
-1xy + 6y + 4y2 = xy + -6y + -1xy + 6y

Reorder the terms:
-1xy + 6y + 4y2 = xy + -1xy + -6y + 6y

Combine like terms: xy + -1xy = 0
-1xy + 6y + 4y2 = 0 + -6y + 6y
-1xy + 6y + 4y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-1xy + 6y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1x + 6 + 4y) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-1x + 6 + 4y)' equal to zero and attempt to solve:

Simplifying
-1x + 6 + 4y = 0

Reorder the terms:
6 + -1x + 4y = 0

Solving
6 + -1x + 4y = 0

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

Add '-6' to each side of the equation.
6 + -1x + -6 + 4y = 0 + -6

Reorder the terms:
6 + -6 + -1x + 4y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x + 4y = 0 + -6
-1x + 4y = 0 + -6

Combine like terms: 0 + -6 = -6
-1x + 4y = -6

Add 'x' to each side of the equation.
-1x + x + 4y = -6 + x

Combine like terms: -1x + x = 0
0 + 4y = -6 + x
4y = -6 + x

Divide each side by '4'.
y = -1.5 + 0.25x

Simplifying
y = -1.5 + 0.25x
Solution
y = {0, -1.5 + 0.25x}