13-[5+5y-3(y+3)]=-3(4y-7)-[8(y-1)-16y+18]

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Solution for 13-[5+5y-3(y+3)]=-3(4y-7)-[8(y-1)-16y+18] equation: 


Simplifying
13 + -1[5 + 5y + -3(y + 3)] = -3(4y + -7) + -1[8(y + -1) + -16y + 18]

Reorder the terms:
13 + -1[5 + 5y + -3(3 + y)] = -3(4y + -7) + -1[8(y + -1) + -16y + 18]
13 + -1[5 + 5y + (3 * -3 + y * -3)] = -3(4y + -7) + -1[8(y + -1) + -16y + 18]
13 + -1[5 + 5y + (-9 + -3y)] = -3(4y + -7) + -1[8(y + -1) + -16y + 18]

Reorder the terms:
13 + -1[5 + -9 + 5y + -3y] = -3(4y + -7) + -1[8(y + -1) + -16y + 18]

Combine like terms: 5 + -9 = -4
13 + -1[-4 + 5y + -3y] = -3(4y + -7) + -1[8(y + -1) + -16y + 18]

Combine like terms: 5y + -3y = 2y
13 + -1[-4 + 2y] = -3(4y + -7) + -1[8(y + -1) + -16y + 18]
13 + [-4 * -1 + 2y * -1] = -3(4y + -7) + -1[8(y + -1) + -16y + 18]
13 + [4 + -2y] = -3(4y + -7) + -1[8(y + -1) + -16y + 18]

Combine like terms: 13 + 4 = 17
17 + -2y = -3(4y + -7) + -1[8(y + -1) + -16y + 18]

Reorder the terms:
17 + -2y = -3(-7 + 4y) + -1[8(y + -1) + -16y + 18]
17 + -2y = (-7 * -3 + 4y * -3) + -1[8(y + -1) + -16y + 18]
17 + -2y = (21 + -12y) + -1[8(y + -1) + -16y + 18]

Reorder the terms:
17 + -2y = 21 + -12y + -1[8(-1 + y) + -16y + 18]
17 + -2y = 21 + -12y + -1[(-1 * 8 + y * 8) + -16y + 18]
17 + -2y = 21 + -12y + -1[(-8 + 8y) + -16y + 18]

Reorder the terms:
17 + -2y = 21 + -12y + -1[-8 + 18 + 8y + -16y]

Combine like terms: -8 + 18 = 10
17 + -2y = 21 + -12y + -1[10 + 8y + -16y]

Combine like terms: 8y + -16y = -8y
17 + -2y = 21 + -12y + -1[10 + -8y]
17 + -2y = 21 + -12y + [10 * -1 + -8y * -1]
17 + -2y = 21 + -12y + [-10 + 8y]

Reorder the terms:
17 + -2y = 21 + -10 + -12y + 8y

Combine like terms: 21 + -10 = 11
17 + -2y = 11 + -12y + 8y

Combine like terms: -12y + 8y = -4y
17 + -2y = 11 + -4y

Solving
17 + -2y = 11 + -4y

Solving for variable 'y'.

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

Add '4y' to each side of the equation.
17 + -2y + 4y = 11 + -4y + 4y

Combine like terms: -2y + 4y = 2y
17 + 2y = 11 + -4y + 4y

Combine like terms: -4y + 4y = 0
17 + 2y = 11 + 0
17 + 2y = 11

Add '-17' to each side of the equation.
17 + -17 + 2y = 11 + -17

Combine like terms: 17 + -17 = 0
0 + 2y = 11 + -17
2y = 11 + -17

Combine like terms: 11 + -17 = -6
2y = -6

Divide each side by '2'.
y = -3

Simplifying
y = -3

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