4(y-1)+5(y+1)=3(y+4)+1

Solution for 4(y-1)+5(y+1)=3(y+4)+1 equation:

Simplifying
4(y + -1) + 5(y + 1) = 3(y + 4) + 1

Reorder the terms:
4(-1 + y) + 5(y + 1) = 3(y + 4) + 1
(-1 * 4 + y * 4) + 5(y + 1) = 3(y + 4) + 1
(-4 + 4y) + 5(y + 1) = 3(y + 4) + 1

Reorder the terms:
-4 + 4y + 5(1 + y) = 3(y + 4) + 1
-4 + 4y + (1 * 5 + y * 5) = 3(y + 4) + 1
-4 + 4y + (5 + 5y) = 3(y + 4) + 1

Reorder the terms:
-4 + 5 + 4y + 5y = 3(y + 4) + 1

Combine like terms: -4 + 5 = 1
1 + 4y + 5y = 3(y + 4) + 1

Combine like terms: 4y + 5y = 9y
1 + 9y = 3(y + 4) + 1

Reorder the terms:
1 + 9y = 3(4 + y) + 1
1 + 9y = (4 * 3 + y * 3) + 1
1 + 9y = (12 + 3y) + 1

Reorder the terms:
1 + 9y = 12 + 1 + 3y

Combine like terms: 12 + 1 = 13
1 + 9y = 13 + 3y

Solving
1 + 9y = 13 + 3y

Solving for variable 'y'.

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

Add '-3y' to each side of the equation.
1 + 9y + -3y = 13 + 3y + -3y

Combine like terms: 9y + -3y = 6y
1 + 6y = 13 + 3y + -3y

Combine like terms: 3y + -3y = 0
1 + 6y = 13 + 0
1 + 6y = 13

Add '-1' to each side of the equation.
1 + -1 + 6y = 13 + -1

Combine like terms: 1 + -1 = 0
0 + 6y = 13 + -1
6y = 13 + -1

Combine like terms: 13 + -1 = 12
6y = 12

Divide each side by '6'.
y = 2

Simplifying
y = 2