45-[4-2y-(y+7)]=-4(1+3y)-[4-3(y+2)-2(2y-5)]

Solution for 45-[4-2y-(y+7)]=-4(1+3y)-[4-3(y+2)-2(2y-5)] equation:

Simplifying
45 + -1[4 + -2y + -1(y + 7)] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]

Reorder the terms:
45 + -1[4 + -2y + -1(7 + y)] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
45 + -1[4 + -2y + (7 * -1 + y * -1)] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
45 + -1[4 + -2y + (-7 + -1y)] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]

Reorder the terms:
45 + -1[4 + -7 + -2y + -1y] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]

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

Combine like terms: -2y + -1y = -3y
45 + -1[-3 + -3y] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
45 + [-3 * -1 + -3y * -1] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
45 + [3 + 3y] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]

Combine like terms: 45 + 3 = 48
48 + 3y = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
48 + 3y = (1 * -4 + 3y * -4) + -1[4 + -3(y + 2) + -2(2y + -5)]
48 + 3y = (-4 + -12y) + -1[4 + -3(y + 2) + -2(2y + -5)]

Reorder the terms:
48 + 3y = -4 + -12y + -1[4 + -3(2 + y) + -2(2y + -5)]
48 + 3y = -4 + -12y + -1[4 + (2 * -3 + y * -3) + -2(2y + -5)]
48 + 3y = -4 + -12y + -1[4 + (-6 + -3y) + -2(2y + -5)]

Reorder the terms:
48 + 3y = -4 + -12y + -1[4 + -6 + -3y + -2(-5 + 2y)]
48 + 3y = -4 + -12y + -1[4 + -6 + -3y + (-5 * -2 + 2y * -2)]
48 + 3y = -4 + -12y + -1[4 + -6 + -3y + (10 + -4y)]

Reorder the terms:
48 + 3y = -4 + -12y + -1[4 + -6 + 10 + -3y + -4y]

Combine like terms: 4 + -6 = -2
48 + 3y = -4 + -12y + -1[-2 + 10 + -3y + -4y]

Combine like terms: -2 + 10 = 8
48 + 3y = -4 + -12y + -1[8 + -3y + -4y]

Combine like terms: -3y + -4y = -7y
48 + 3y = -4 + -12y + -1[8 + -7y]
48 + 3y = -4 + -12y + [8 * -1 + -7y * -1]
48 + 3y = -4 + -12y + [-8 + 7y]

Reorder the terms:
48 + 3y = -4 + -8 + -12y + 7y

Combine like terms: -4 + -8 = -12
48 + 3y = -12 + -12y + 7y

Combine like terms: -12y + 7y = -5y
48 + 3y = -12 + -5y

Solving
48 + 3y = -12 + -5y

Solving for variable 'y'.

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

Add '5y' to each side of the equation.
48 + 3y + 5y = -12 + -5y + 5y

Combine like terms: 3y + 5y = 8y
48 + 8y = -12 + -5y + 5y

Combine like terms: -5y + 5y = 0
48 + 8y = -12 + 0
48 + 8y = -12

Add '-48' to each side of the equation.
48 + -48 + 8y = -12 + -48

Combine like terms: 48 + -48 = 0
0 + 8y = -12 + -48
8y = -12 + -48

Combine like terms: -12 + -48 = -60
8y = -60

Divide each side by '8'.
y = -7.5

Simplifying
y = -7.5