45-[5+7y-2(y+4)]=-5(4y-3)-[9(y-1)-16y+8]

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Solution for 45-[5+7y-2(y+4)]=-5(4y-3)-[9(y-1)-16y+8] equation: 


Simplifying
45 + -1[5 + 7y + -2(y + 4)] = -5(4y + -3) + -1[9(y + -1) + -16y + 8]

Reorder the terms:
45 + -1[5 + 7y + -2(4 + y)] = -5(4y + -3) + -1[9(y + -1) + -16y + 8]
45 + -1[5 + 7y + (4 * -2 + y * -2)] = -5(4y + -3) + -1[9(y + -1) + -16y + 8]
45 + -1[5 + 7y + (-8 + -2y)] = -5(4y + -3) + -1[9(y + -1) + -16y + 8]

Reorder the terms:
45 + -1[5 + -8 + 7y + -2y] = -5(4y + -3) + -1[9(y + -1) + -16y + 8]

Combine like terms: 5 + -8 = -3
45 + -1[-3 + 7y + -2y] = -5(4y + -3) + -1[9(y + -1) + -16y + 8]

Combine like terms: 7y + -2y = 5y
45 + -1[-3 + 5y] = -5(4y + -3) + -1[9(y + -1) + -16y + 8]
45 + [-3 * -1 + 5y * -1] = -5(4y + -3) + -1[9(y + -1) + -16y + 8]
45 + [3 + -5y] = -5(4y + -3) + -1[9(y + -1) + -16y + 8]

Combine like terms: 45 + 3 = 48
48 + -5y = -5(4y + -3) + -1[9(y + -1) + -16y + 8]

Reorder the terms:
48 + -5y = -5(-3 + 4y) + -1[9(y + -1) + -16y + 8]
48 + -5y = (-3 * -5 + 4y * -5) + -1[9(y + -1) + -16y + 8]
48 + -5y = (15 + -20y) + -1[9(y + -1) + -16y + 8]

Reorder the terms:
48 + -5y = 15 + -20y + -1[9(-1 + y) + -16y + 8]
48 + -5y = 15 + -20y + -1[(-1 * 9 + y * 9) + -16y + 8]
48 + -5y = 15 + -20y + -1[(-9 + 9y) + -16y + 8]

Reorder the terms:
48 + -5y = 15 + -20y + -1[-9 + 8 + 9y + -16y]

Combine like terms: -9 + 8 = -1
48 + -5y = 15 + -20y + -1[-1 + 9y + -16y]

Combine like terms: 9y + -16y = -7y
48 + -5y = 15 + -20y + -1[-1 + -7y]
48 + -5y = 15 + -20y + [-1 * -1 + -7y * -1]
48 + -5y = 15 + -20y + [1 + 7y]

Reorder the terms:
48 + -5y = 15 + 1 + -20y + 7y

Combine like terms: 15 + 1 = 16
48 + -5y = 16 + -20y + 7y

Combine like terms: -20y + 7y = -13y
48 + -5y = 16 + -13y

Solving
48 + -5y = 16 + -13y

Solving for variable 'y'.

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

Add '13y' to each side of the equation.
48 + -5y + 13y = 16 + -13y + 13y

Combine like terms: -5y + 13y = 8y
48 + 8y = 16 + -13y + 13y

Combine like terms: -13y + 13y = 0
48 + 8y = 16 + 0
48 + 8y = 16

Add '-48' to each side of the equation.
48 + -48 + 8y = 16 + -48

Combine like terms: 48 + -48 = 0
0 + 8y = 16 + -48
8y = 16 + -48

Combine like terms: 16 + -48 = -32
8y = -32

Divide each side by '8'.
y = -4

Simplifying
y = -4

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