27-[1+8y-2(y+4)]=-4(4y-7)-[5(y-1)-7y+15]

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Solution for 27-[1+8y-2(y+4)]=-4(4y-7)-[5(y-1)-7y+15] equation: 


Simplifying
27 + -1[1 + 8y + -2(y + 4)] = -4(4y + -7) + -1[5(y + -1) + -7y + 15]

Reorder the terms:
27 + -1[1 + 8y + -2(4 + y)] = -4(4y + -7) + -1[5(y + -1) + -7y + 15]
27 + -1[1 + 8y + (4 * -2 + y * -2)] = -4(4y + -7) + -1[5(y + -1) + -7y + 15]
27 + -1[1 + 8y + (-8 + -2y)] = -4(4y + -7) + -1[5(y + -1) + -7y + 15]

Reorder the terms:
27 + -1[1 + -8 + 8y + -2y] = -4(4y + -7) + -1[5(y + -1) + -7y + 15]

Combine like terms: 1 + -8 = -7
27 + -1[-7 + 8y + -2y] = -4(4y + -7) + -1[5(y + -1) + -7y + 15]

Combine like terms: 8y + -2y = 6y
27 + -1[-7 + 6y] = -4(4y + -7) + -1[5(y + -1) + -7y + 15]
27 + [-7 * -1 + 6y * -1] = -4(4y + -7) + -1[5(y + -1) + -7y + 15]
27 + [7 + -6y] = -4(4y + -7) + -1[5(y + -1) + -7y + 15]

Combine like terms: 27 + 7 = 34
34 + -6y = -4(4y + -7) + -1[5(y + -1) + -7y + 15]

Reorder the terms:
34 + -6y = -4(-7 + 4y) + -1[5(y + -1) + -7y + 15]
34 + -6y = (-7 * -4 + 4y * -4) + -1[5(y + -1) + -7y + 15]
34 + -6y = (28 + -16y) + -1[5(y + -1) + -7y + 15]

Reorder the terms:
34 + -6y = 28 + -16y + -1[5(-1 + y) + -7y + 15]
34 + -6y = 28 + -16y + -1[(-1 * 5 + y * 5) + -7y + 15]
34 + -6y = 28 + -16y + -1[(-5 + 5y) + -7y + 15]

Reorder the terms:
34 + -6y = 28 + -16y + -1[-5 + 15 + 5y + -7y]

Combine like terms: -5 + 15 = 10
34 + -6y = 28 + -16y + -1[10 + 5y + -7y]

Combine like terms: 5y + -7y = -2y
34 + -6y = 28 + -16y + -1[10 + -2y]
34 + -6y = 28 + -16y + [10 * -1 + -2y * -1]
34 + -6y = 28 + -16y + [-10 + 2y]

Reorder the terms:
34 + -6y = 28 + -10 + -16y + 2y

Combine like terms: 28 + -10 = 18
34 + -6y = 18 + -16y + 2y

Combine like terms: -16y + 2y = -14y
34 + -6y = 18 + -14y

Solving
34 + -6y = 18 + -14y

Solving for variable 'y'.

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

Add '14y' to each side of the equation.
34 + -6y + 14y = 18 + -14y + 14y

Combine like terms: -6y + 14y = 8y
34 + 8y = 18 + -14y + 14y

Combine like terms: -14y + 14y = 0
34 + 8y = 18 + 0
34 + 8y = 18

Add '-34' to each side of the equation.
34 + -34 + 8y = 18 + -34

Combine like terms: 34 + -34 = 0
0 + 8y = 18 + -34
8y = 18 + -34

Combine like terms: 18 + -34 = -16
8y = -16

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

Simplifying
y = -2

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