15-[1+7y-2(y+5)]=-4(4y-6)-[9(y-1)-16y+17]

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Solution for 15-[1+7y-2(y+5)]=-4(4y-6)-[9(y-1)-16y+17] equation:


Simplifying
15 + -1[1 + 7y + -2(y + 5)] = -4(4y + -6) + -1[9(y + -1) + -16y + 17]

Reorder the terms:
15 + -1[1 + 7y + -2(5 + y)] = -4(4y + -6) + -1[9(y + -1) + -16y + 17]
15 + -1[1 + 7y + (5 * -2 + y * -2)] = -4(4y + -6) + -1[9(y + -1) + -16y + 17]
15 + -1[1 + 7y + (-10 + -2y)] = -4(4y + -6) + -1[9(y + -1) + -16y + 17]

Reorder the terms:
15 + -1[1 + -10 + 7y + -2y] = -4(4y + -6) + -1[9(y + -1) + -16y + 17]

Combine like terms: 1 + -10 = -9
15 + -1[-9 + 7y + -2y] = -4(4y + -6) + -1[9(y + -1) + -16y + 17]

Combine like terms: 7y + -2y = 5y
15 + -1[-9 + 5y] = -4(4y + -6) + -1[9(y + -1) + -16y + 17]
15 + [-9 * -1 + 5y * -1] = -4(4y + -6) + -1[9(y + -1) + -16y + 17]
15 + [9 + -5y] = -4(4y + -6) + -1[9(y + -1) + -16y + 17]

Combine like terms: 15 + 9 = 24
24 + -5y = -4(4y + -6) + -1[9(y + -1) + -16y + 17]

Reorder the terms:
24 + -5y = -4(-6 + 4y) + -1[9(y + -1) + -16y + 17]
24 + -5y = (-6 * -4 + 4y * -4) + -1[9(y + -1) + -16y + 17]
24 + -5y = (24 + -16y) + -1[9(y + -1) + -16y + 17]

Reorder the terms:
24 + -5y = 24 + -16y + -1[9(-1 + y) + -16y + 17]
24 + -5y = 24 + -16y + -1[(-1 * 9 + y * 9) + -16y + 17]
24 + -5y = 24 + -16y + -1[(-9 + 9y) + -16y + 17]

Reorder the terms:
24 + -5y = 24 + -16y + -1[-9 + 17 + 9y + -16y]

Combine like terms: -9 + 17 = 8
24 + -5y = 24 + -16y + -1[8 + 9y + -16y]

Combine like terms: 9y + -16y = -7y
24 + -5y = 24 + -16y + -1[8 + -7y]
24 + -5y = 24 + -16y + [8 * -1 + -7y * -1]
24 + -5y = 24 + -16y + [-8 + 7y]

Reorder the terms:
24 + -5y = 24 + -8 + -16y + 7y

Combine like terms: 24 + -8 = 16
24 + -5y = 16 + -16y + 7y

Combine like terms: -16y + 7y = -9y
24 + -5y = 16 + -9y

Solving
24 + -5y = 16 + -9y

Solving for variable 'y'.

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

Add '9y' to each side of the equation.
24 + -5y + 9y = 16 + -9y + 9y

Combine like terms: -5y + 9y = 4y
24 + 4y = 16 + -9y + 9y

Combine like terms: -9y + 9y = 0
24 + 4y = 16 + 0
24 + 4y = 16

Add '-24' to each side of the equation.
24 + -24 + 4y = 16 + -24

Combine like terms: 24 + -24 = 0
0 + 4y = 16 + -24
4y = 16 + -24

Combine like terms: 16 + -24 = -8
4y = -8

Divide each side by '4'.
y = -2

Simplifying
y = -2

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