(-8y+3)+(2y-9)=(ny-6)

Solution for (-8y+3)+(2y-9)=(ny-6) equation:

Simplifying
(-8y + 3) + (2y + -9) = (ny + -6)

Reorder the terms:
(3 + -8y) + (2y + -9) = (ny + -6)

Remove parenthesis around (3 + -8y)
3 + -8y + (2y + -9) = (ny + -6)

Reorder the terms:
3 + -8y + (-9 + 2y) = (ny + -6)

Remove parenthesis around (-9 + 2y)
3 + -8y + -9 + 2y = (ny + -6)

Reorder the terms:
3 + -9 + -8y + 2y = (ny + -6)

Combine like terms: 3 + -9 = -6
-6 + -8y + 2y = (ny + -6)

Combine like terms: -8y + 2y = -6y
-6 + -6y = (ny + -6)

Reorder the terms:
-6 + -6y = (-6 + ny)

Remove parenthesis around (-6 + ny)
-6 + -6y = -6 + ny

Add '6' to each side of the equation.
-6 + 6 + -6y = -6 + 6 + ny

Combine like terms: -6 + 6 = 0
0 + -6y = -6 + 6 + ny
-6y = -6 + 6 + ny

Combine like terms: -6 + 6 = 0
-6y = 0 + ny
-6y = ny

Solving
-6y = ny

Solving for variable 'y'.

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

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

Combine like terms: ny + -1ny = 0
-1ny + -6y = 0

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

Ignore the factor -1.
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 '(n + 6)' equal to zero and attempt to solve:

Simplifying
n + 6 = 0

Reorder the terms:
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Add '-1n' to each side of the equation.
n + -1n = -6 + -1n

Combine like terms: n + -1n = 0
0 = -6 + -1n

Simplifying
0 = -6 + -1n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}