3y=2(y-3)-4(2y+1)

Solution for 3y=2(y-3)-4(2y+1) equation:

Simplifying
3y = 2(y + -3) + -4(2y + 1)

Reorder the terms:
3y = 2(-3 + y) + -4(2y + 1)
3y = (-3 * 2 + y * 2) + -4(2y + 1)
3y = (-6 + 2y) + -4(2y + 1)

Reorder the terms:
3y = -6 + 2y + -4(1 + 2y)
3y = -6 + 2y + (1 * -4 + 2y * -4)
3y = -6 + 2y + (-4 + -8y)

Reorder the terms:
3y = -6 + -4 + 2y + -8y

Combine like terms: -6 + -4 = -10
3y = -10 + 2y + -8y

Combine like terms: 2y + -8y = -6y
3y = -10 + -6y

Solving
3y = -10 + -6y

Solving for variable 'y'.

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

Add '6y' to each side of the equation.
3y + 6y = -10 + -6y + 6y

Combine like terms: 3y + 6y = 9y
9y = -10 + -6y + 6y

Combine like terms: -6y + 6y = 0
9y = -10 + 0
9y = -10

Divide each side by '9'.
y = -1.111111111

Simplifying
y = -1.111111111