3y+1-5(-3y-1)=2(y-3)

Solution for 3y+1-5(-3y-1)=2(y-3) equation:

Simplifying
3y + 1 + -5(-3y + -1) = 2(y + -3)

Reorder the terms:
3y + 1 + -5(-1 + -3y) = 2(y + -3)
3y + 1 + (-1 * -5 + -3y * -5) = 2(y + -3)
3y + 1 + (5 + 15y) = 2(y + -3)

Reorder the terms:
1 + 5 + 3y + 15y = 2(y + -3)

Combine like terms: 1 + 5 = 6
6 + 3y + 15y = 2(y + -3)

Combine like terms: 3y + 15y = 18y
6 + 18y = 2(y + -3)

Reorder the terms:
6 + 18y = 2(-3 + y)
6 + 18y = (-3 * 2 + y * 2)
6 + 18y = (-6 + 2y)

Solving
6 + 18y = -6 + 2y

Solving for variable 'y'.

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

Add '-2y' to each side of the equation.
6 + 18y + -2y = -6 + 2y + -2y

Combine like terms: 18y + -2y = 16y
6 + 16y = -6 + 2y + -2y

Combine like terms: 2y + -2y = 0
6 + 16y = -6 + 0
6 + 16y = -6

Add '-6' to each side of the equation.
6 + -6 + 16y = -6 + -6

Combine like terms: 6 + -6 = 0
0 + 16y = -6 + -6
16y = -6 + -6

Combine like terms: -6 + -6 = -12
16y = -12

Divide each side by '16'.
y = -0.75

Simplifying
y = -0.75