45-(2+6y-2(y+3))=-3(5y-1)-(5(y-1)-7y+13)

Solution for 45-(2+6y-2(y+3))=-3(5y-1)-(5(y-1)-7y+13) equation:

Simplifying
45 + -1(2 + 6y + -2(y + 3)) = -3(5y + -1) + -1(5(y + -1) + -7y + 13)

Reorder the terms:
45 + -1(2 + 6y + -2(3 + y)) = -3(5y + -1) + -1(5(y + -1) + -7y + 13)
45 + -1(2 + 6y + (3 * -2 + y * -2)) = -3(5y + -1) + -1(5(y + -1) + -7y + 13)
45 + -1(2 + 6y + (-6 + -2y)) = -3(5y + -1) + -1(5(y + -1) + -7y + 13)

Reorder the terms:
45 + -1(2 + -6 + 6y + -2y) = -3(5y + -1) + -1(5(y + -1) + -7y + 13)

Combine like terms: 2 + -6 = -4
45 + -1(-4 + 6y + -2y) = -3(5y + -1) + -1(5(y + -1) + -7y + 13)

Combine like terms: 6y + -2y = 4y
45 + -1(-4 + 4y) = -3(5y + -1) + -1(5(y + -1) + -7y + 13)
45 + (-4 * -1 + 4y * -1) = -3(5y + -1) + -1(5(y + -1) + -7y + 13)
45 + (4 + -4y) = -3(5y + -1) + -1(5(y + -1) + -7y + 13)

Combine like terms: 45 + 4 = 49
49 + -4y = -3(5y + -1) + -1(5(y + -1) + -7y + 13)

Reorder the terms:
49 + -4y = -3(-1 + 5y) + -1(5(y + -1) + -7y + 13)
49 + -4y = (-1 * -3 + 5y * -3) + -1(5(y + -1) + -7y + 13)
49 + -4y = (3 + -15y) + -1(5(y + -1) + -7y + 13)

Reorder the terms:
49 + -4y = 3 + -15y + -1(5(-1 + y) + -7y + 13)
49 + -4y = 3 + -15y + -1((-1 * 5 + y * 5) + -7y + 13)
49 + -4y = 3 + -15y + -1((-5 + 5y) + -7y + 13)

Reorder the terms:
49 + -4y = 3 + -15y + -1(-5 + 13 + 5y + -7y)

Combine like terms: -5 + 13 = 8
49 + -4y = 3 + -15y + -1(8 + 5y + -7y)

Combine like terms: 5y + -7y = -2y
49 + -4y = 3 + -15y + -1(8 + -2y)
49 + -4y = 3 + -15y + (8 * -1 + -2y * -1)
49 + -4y = 3 + -15y + (-8 + 2y)

Reorder the terms:
49 + -4y = 3 + -8 + -15y + 2y

Combine like terms: 3 + -8 = -5
49 + -4y = -5 + -15y + 2y

Combine like terms: -15y + 2y = -13y
49 + -4y = -5 + -13y

Solving
49 + -4y = -5 + -13y

Solving for variable 'y'.

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

Add '13y' to each side of the equation.
49 + -4y + 13y = -5 + -13y + 13y

Combine like terms: -4y + 13y = 9y
49 + 9y = -5 + -13y + 13y

Combine like terms: -13y + 13y = 0
49 + 9y = -5 + 0
49 + 9y = -5

Add '-49' to each side of the equation.
49 + -49 + 9y = -5 + -49

Combine like terms: 49 + -49 = 0
0 + 9y = -5 + -49
9y = -5 + -49

Combine like terms: -5 + -49 = -54
9y = -54

Divide each side by '9'.
y = -6

Simplifying
y = -6