Y+1-2(-7Y-1)=3(Y-1)

Solution for Y+1-2(-7Y-1)=3(Y-1) equation:

Simplifying
Y + 1 + -2(-7Y + -1) = 3(Y + -1)

Reorder the terms:
Y + 1 + -2(-1 + -7Y) = 3(Y + -1)
Y + 1 + (-1 * -2 + -7Y * -2) = 3(Y + -1)
Y + 1 + (2 + 14Y) = 3(Y + -1)

Reorder the terms:
1 + 2 + Y + 14Y = 3(Y + -1)

Combine like terms: 1 + 2 = 3
3 + Y + 14Y = 3(Y + -1)

Combine like terms: Y + 14Y = 15Y
3 + 15Y = 3(Y + -1)

Reorder the terms:
3 + 15Y = 3(-1 + Y)
3 + 15Y = (-1 * 3 + Y * 3)
3 + 15Y = (-3 + 3Y)

Solving
3 + 15Y = -3 + 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.
3 + 15Y + -3Y = -3 + 3Y + -3Y

Combine like terms: 15Y + -3Y = 12Y
3 + 12Y = -3 + 3Y + -3Y

Combine like terms: 3Y + -3Y = 0
3 + 12Y = -3 + 0
3 + 12Y = -3

Add '-3' to each side of the equation.
3 + -3 + 12Y = -3 + -3

Combine like terms: 3 + -3 = 0
0 + 12Y = -3 + -3
12Y = -3 + -3

Combine like terms: -3 + -3 = -6
12Y = -6

Divide each side by '12'.
Y = -0.5

Simplifying
Y = -0.5