(y+2)+(3y-5)=(ny-3)

Solution for (y+2)+(3y-5)=(ny-3) equation:

Simplifying
(y + 2) + (3y + -5) = (ny + -3)

Reorder the terms:
(2 + y) + (3y + -5) = (ny + -3)

Remove parenthesis around (2 + y)
2 + y + (3y + -5) = (ny + -3)

Reorder the terms:
2 + y + (-5 + 3y) = (ny + -3)

Remove parenthesis around (-5 + 3y)
2 + y + -5 + 3y = (ny + -3)

Reorder the terms:
2 + -5 + y + 3y = (ny + -3)

Combine like terms: 2 + -5 = -3
-3 + y + 3y = (ny + -3)

Combine like terms: y + 3y = 4y
-3 + 4y = (ny + -3)

Reorder the terms:
-3 + 4y = (-3 + ny)

Remove parenthesis around (-3 + ny)
-3 + 4y = -3 + ny

Add '3' to each side of the equation.
-3 + 3 + 4y = -3 + 3 + ny

Combine like terms: -3 + 3 = 0
0 + 4y = -3 + 3 + ny
4y = -3 + 3 + ny

Combine like terms: -3 + 3 = 0
4y = 0 + ny
4y = ny

Solving
4y = 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 + 4y = ny + -1ny

Combine like terms: ny + -1ny = 0
-1ny + 4y = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1n + 4) = 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 '(-1n + 4)' equal to zero and attempt to solve:

Simplifying
-1n + 4 = 0

Reorder the terms:
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Add 'n' to each side of the equation.
-1n + n = -4 + n

Combine like terms: -1n + n = 0
0 = -4 + n

Simplifying
0 = -4 + n

The solution to this equation could not be determined.

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