(7y+6)+(3y-2)=(ny+4)

Solution for (7y+6)+(3y-2)=(ny+4) equation:

Simplifying
(7y + 6) + (3y + -2) = (ny + 4)

Reorder the terms:
(6 + 7y) + (3y + -2) = (ny + 4)

Remove parenthesis around (6 + 7y)
6 + 7y + (3y + -2) = (ny + 4)

Reorder the terms:
6 + 7y + (-2 + 3y) = (ny + 4)

Remove parenthesis around (-2 + 3y)
6 + 7y + -2 + 3y = (ny + 4)

Reorder the terms:
6 + -2 + 7y + 3y = (ny + 4)

Combine like terms: 6 + -2 = 4
4 + 7y + 3y = (ny + 4)

Combine like terms: 7y + 3y = 10y
4 + 10y = (ny + 4)

Reorder the terms:
4 + 10y = (4 + ny)

Remove parenthesis around (4 + ny)
4 + 10y = 4 + ny

Add '-4' to each side of the equation.
4 + -4 + 10y = 4 + -4 + ny

Combine like terms: 4 + -4 = 0
0 + 10y = 4 + -4 + ny
10y = 4 + -4 + ny

Combine like terms: 4 + -4 = 0
10y = 0 + ny
10y = ny

Solving
10y = 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 + 10y = ny + -1ny

Combine like terms: ny + -1ny = 0
-1ny + 10y = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1n + 10) = 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 + 10)' equal to zero and attempt to solve:

Simplifying
-1n + 10 = 0

Reorder the terms:
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Add 'n' to each side of the equation.
-1n + n = -10 + n

Combine like terms: -1n + n = 0
0 = -10 + n

Simplifying
0 = -10 + 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}