30-[1+5y-2(y+2)]=-5(3y-4)-[8(y-1)-18y+11]

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Solution for 30-[1+5y-2(y+2)]=-5(3y-4)-[8(y-1)-18y+11] equation: 


Simplifying
30 + -1[1 + 5y + -2(y + 2)] = -5(3y + -4) + -1[8(y + -1) + -18y + 11]

Reorder the terms:
30 + -1[1 + 5y + -2(2 + y)] = -5(3y + -4) + -1[8(y + -1) + -18y + 11]
30 + -1[1 + 5y + (2 * -2 + y * -2)] = -5(3y + -4) + -1[8(y + -1) + -18y + 11]
30 + -1[1 + 5y + (-4 + -2y)] = -5(3y + -4) + -1[8(y + -1) + -18y + 11]

Reorder the terms:
30 + -1[1 + -4 + 5y + -2y] = -5(3y + -4) + -1[8(y + -1) + -18y + 11]

Combine like terms: 1 + -4 = -3
30 + -1[-3 + 5y + -2y] = -5(3y + -4) + -1[8(y + -1) + -18y + 11]

Combine like terms: 5y + -2y = 3y
30 + -1[-3 + 3y] = -5(3y + -4) + -1[8(y + -1) + -18y + 11]
30 + [-3 * -1 + 3y * -1] = -5(3y + -4) + -1[8(y + -1) + -18y + 11]
30 + [3 + -3y] = -5(3y + -4) + -1[8(y + -1) + -18y + 11]

Combine like terms: 30 + 3 = 33
33 + -3y = -5(3y + -4) + -1[8(y + -1) + -18y + 11]

Reorder the terms:
33 + -3y = -5(-4 + 3y) + -1[8(y + -1) + -18y + 11]
33 + -3y = (-4 * -5 + 3y * -5) + -1[8(y + -1) + -18y + 11]
33 + -3y = (20 + -15y) + -1[8(y + -1) + -18y + 11]

Reorder the terms:
33 + -3y = 20 + -15y + -1[8(-1 + y) + -18y + 11]
33 + -3y = 20 + -15y + -1[(-1 * 8 + y * 8) + -18y + 11]
33 + -3y = 20 + -15y + -1[(-8 + 8y) + -18y + 11]

Reorder the terms:
33 + -3y = 20 + -15y + -1[-8 + 11 + 8y + -18y]

Combine like terms: -8 + 11 = 3
33 + -3y = 20 + -15y + -1[3 + 8y + -18y]

Combine like terms: 8y + -18y = -10y
33 + -3y = 20 + -15y + -1[3 + -10y]
33 + -3y = 20 + -15y + [3 * -1 + -10y * -1]
33 + -3y = 20 + -15y + [-3 + 10y]

Reorder the terms:
33 + -3y = 20 + -3 + -15y + 10y

Combine like terms: 20 + -3 = 17
33 + -3y = 17 + -15y + 10y

Combine like terms: -15y + 10y = -5y
33 + -3y = 17 + -5y

Solving
33 + -3y = 17 + -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.
33 + -3y + 5y = 17 + -5y + 5y

Combine like terms: -3y + 5y = 2y
33 + 2y = 17 + -5y + 5y

Combine like terms: -5y + 5y = 0
33 + 2y = 17 + 0
33 + 2y = 17

Add '-33' to each side of the equation.
33 + -33 + 2y = 17 + -33

Combine like terms: 33 + -33 = 0
0 + 2y = 17 + -33
2y = 17 + -33

Combine like terms: 17 + -33 = -16
2y = -16

Divide each side by '2'.
y = -8

Simplifying
y = -8

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