40-[4+8y-3(y+2)]=-3(5y-7)-[8(y-1)-13y+17]

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Solution for 40-[4+8y-3(y+2)]=-3(5y-7)-[8(y-1)-13y+17] equation: 


Simplifying
40 + -1[4 + 8y + -3(y + 2)] = -3(5y + -7) + -1[8(y + -1) + -13y + 17]

Reorder the terms:
40 + -1[4 + 8y + -3(2 + y)] = -3(5y + -7) + -1[8(y + -1) + -13y + 17]
40 + -1[4 + 8y + (2 * -3 + y * -3)] = -3(5y + -7) + -1[8(y + -1) + -13y + 17]
40 + -1[4 + 8y + (-6 + -3y)] = -3(5y + -7) + -1[8(y + -1) + -13y + 17]

Reorder the terms:
40 + -1[4 + -6 + 8y + -3y] = -3(5y + -7) + -1[8(y + -1) + -13y + 17]

Combine like terms: 4 + -6 = -2
40 + -1[-2 + 8y + -3y] = -3(5y + -7) + -1[8(y + -1) + -13y + 17]

Combine like terms: 8y + -3y = 5y
40 + -1[-2 + 5y] = -3(5y + -7) + -1[8(y + -1) + -13y + 17]
40 + [-2 * -1 + 5y * -1] = -3(5y + -7) + -1[8(y + -1) + -13y + 17]
40 + [2 + -5y] = -3(5y + -7) + -1[8(y + -1) + -13y + 17]

Combine like terms: 40 + 2 = 42
42 + -5y = -3(5y + -7) + -1[8(y + -1) + -13y + 17]

Reorder the terms:
42 + -5y = -3(-7 + 5y) + -1[8(y + -1) + -13y + 17]
42 + -5y = (-7 * -3 + 5y * -3) + -1[8(y + -1) + -13y + 17]
42 + -5y = (21 + -15y) + -1[8(y + -1) + -13y + 17]

Reorder the terms:
42 + -5y = 21 + -15y + -1[8(-1 + y) + -13y + 17]
42 + -5y = 21 + -15y + -1[(-1 * 8 + y * 8) + -13y + 17]
42 + -5y = 21 + -15y + -1[(-8 + 8y) + -13y + 17]

Reorder the terms:
42 + -5y = 21 + -15y + -1[-8 + 17 + 8y + -13y]

Combine like terms: -8 + 17 = 9
42 + -5y = 21 + -15y + -1[9 + 8y + -13y]

Combine like terms: 8y + -13y = -5y
42 + -5y = 21 + -15y + -1[9 + -5y]
42 + -5y = 21 + -15y + [9 * -1 + -5y * -1]
42 + -5y = 21 + -15y + [-9 + 5y]

Reorder the terms:
42 + -5y = 21 + -9 + -15y + 5y

Combine like terms: 21 + -9 = 12
42 + -5y = 12 + -15y + 5y

Combine like terms: -15y + 5y = -10y
42 + -5y = 12 + -10y

Solving
42 + -5y = 12 + -10y

Solving for variable 'y'.

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

Add '10y' to each side of the equation.
42 + -5y + 10y = 12 + -10y + 10y

Combine like terms: -5y + 10y = 5y
42 + 5y = 12 + -10y + 10y

Combine like terms: -10y + 10y = 0
42 + 5y = 12 + 0
42 + 5y = 12

Add '-42' to each side of the equation.
42 + -42 + 5y = 12 + -42

Combine like terms: 42 + -42 = 0
0 + 5y = 12 + -42
5y = 12 + -42

Combine like terms: 12 + -42 = -30
5y = -30

Divide each side by '5'.
y = -6

Simplifying
y = -6

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