9(x+2)y^2+48(x+2)y-36(x+2)=0

Solution for 9(x+2)y^2+48(x+2)y-36(x+2)=0 equation:

Simplifying
9(x + 2) * y2 + 48(x + 2) * y + -36(x + 2) = 0

Reorder the terms:
9(2 + x) * y2 + 48(x + 2) * y + -36(x + 2) = 0

Reorder the terms for easier multiplication:
9y2(2 + x) + 48(x + 2) * y + -36(x + 2) = 0
(2 * 9y2 + x * 9y2) + 48(x + 2) * y + -36(x + 2) = 0

Reorder the terms:
(9xy2 + 18y2) + 48(x + 2) * y + -36(x + 2) = 0
(9xy2 + 18y2) + 48(x + 2) * y + -36(x + 2) = 0

Reorder the terms:
9xy2 + 18y2 + 48(2 + x) * y + -36(x + 2) = 0

Reorder the terms for easier multiplication:
9xy2 + 18y2 + 48y(2 + x) + -36(x + 2) = 0
9xy2 + 18y2 + (2 * 48y + x * 48y) + -36(x + 2) = 0

Reorder the terms:
9xy2 + 18y2 + (48xy + 96y) + -36(x + 2) = 0
9xy2 + 18y2 + (48xy + 96y) + -36(x + 2) = 0

Reorder the terms:
9xy2 + 18y2 + 48xy + 96y + -36(2 + x) = 0
9xy2 + 18y2 + 48xy + 96y + (2 * -36 + x * -36) = 0
9xy2 + 18y2 + 48xy + 96y + (-72 + -36x) = 0

Reorder the terms:
-72 + -36x + 48xy + 9xy2 + 96y + 18y2 = 0

Solving
-72 + -36x + 48xy + 9xy2 + 96y + 18y2 = 0

Solving for variable 'x'.

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

Add '72' to each side of the equation.
-72 + -36x + 48xy + 9xy2 + 96y + 72 + 18y2 = 0 + 72

Reorder the terms:
-72 + 72 + -36x + 48xy + 9xy2 + 96y + 18y2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -36x + 48xy + 9xy2 + 96y + 18y2 = 0 + 72
-36x + 48xy + 9xy2 + 96y + 18y2 = 0 + 72

Combine like terms: 0 + 72 = 72
-36x + 48xy + 9xy2 + 96y + 18y2 = 72

Add '-96y' to each side of the equation.
-36x + 48xy + 9xy2 + 96y + -96y + 18y2 = 72 + -96y

Combine like terms: 96y + -96y = 0
-36x + 48xy + 9xy2 + 0 + 18y2 = 72 + -96y
-36x + 48xy + 9xy2 + 18y2 = 72 + -96y

Add '-18y2' to each side of the equation.
-36x + 48xy + 9xy2 + 18y2 + -18y2 = 72 + -96y + -18y2

Combine like terms: 18y2 + -18y2 = 0
-36x + 48xy + 9xy2 + 0 = 72 + -96y + -18y2
-36x + 48xy + 9xy2 = 72 + -96y + -18y2

Reorder the terms:
-72 + -36x + 48xy + 9xy2 + 96y + 18y2 = 72 + -96y + -18y2 + -72 + 96y + 18y2

Reorder the terms:
-72 + -36x + 48xy + 9xy2 + 96y + 18y2 = 72 + -72 + -96y + 96y + -18y2 + 18y2

Combine like terms: 72 + -72 = 0
-72 + -36x + 48xy + 9xy2 + 96y + 18y2 = 0 + -96y + 96y + -18y2 + 18y2
-72 + -36x + 48xy + 9xy2 + 96y + 18y2 = -96y + 96y + -18y2 + 18y2

Combine like terms: -96y + 96y = 0
-72 + -36x + 48xy + 9xy2 + 96y + 18y2 = 0 + -18y2 + 18y2
-72 + -36x + 48xy + 9xy2 + 96y + 18y2 = -18y2 + 18y2

Combine like terms: -18y2 + 18y2 = 0
-72 + -36x + 48xy + 9xy2 + 96y + 18y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -12x + 16xy + 3xy2 + 32y + 6y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-24 + -12x + 16xy + 3xy2 + 32y + 6y2)' equal to zero and attempt to solve:

Simplifying
-24 + -12x + 16xy + 3xy2 + 32y + 6y2 = 0

Solving
-24 + -12x + 16xy + 3xy2 + 32y + 6y2 = 0

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

Add '24' to each side of the equation.
-24 + -12x + 16xy + 3xy2 + 32y + 24 + 6y2 = 0 + 24

Reorder the terms:
-24 + 24 + -12x + 16xy + 3xy2 + 32y + 6y2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -12x + 16xy + 3xy2 + 32y + 6y2 = 0 + 24
-12x + 16xy + 3xy2 + 32y + 6y2 = 0 + 24

Combine like terms: 0 + 24 = 24
-12x + 16xy + 3xy2 + 32y + 6y2 = 24

Add '-32y' to each side of the equation.
-12x + 16xy + 3xy2 + 32y + -32y + 6y2 = 24 + -32y

Combine like terms: 32y + -32y = 0
-12x + 16xy + 3xy2 + 0 + 6y2 = 24 + -32y
-12x + 16xy + 3xy2 + 6y2 = 24 + -32y

Add '-6y2' to each side of the equation.
-12x + 16xy + 3xy2 + 6y2 + -6y2 = 24 + -32y + -6y2

Combine like terms: 6y2 + -6y2 = 0
-12x + 16xy + 3xy2 + 0 = 24 + -32y + -6y2
-12x + 16xy + 3xy2 = 24 + -32y + -6y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.