46-[5+4y-2(y+3)]=-4(4y-3)-[9(y-1)-18y+4]

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Solution for 46-[5+4y-2(y+3)]=-4(4y-3)-[9(y-1)-18y+4] equation:


Simplifying
46 + -1[5 + 4y + -2(y + 3)] = -4(4y + -3) + -1[9(y + -1) + -18y + 4]

Reorder the terms:
46 + -1[5 + 4y + -2(3 + y)] = -4(4y + -3) + -1[9(y + -1) + -18y + 4]
46 + -1[5 + 4y + (3 * -2 + y * -2)] = -4(4y + -3) + -1[9(y + -1) + -18y + 4]
46 + -1[5 + 4y + (-6 + -2y)] = -4(4y + -3) + -1[9(y + -1) + -18y + 4]

Reorder the terms:
46 + -1[5 + -6 + 4y + -2y] = -4(4y + -3) + -1[9(y + -1) + -18y + 4]

Combine like terms: 5 + -6 = -1
46 + -1[-1 + 4y + -2y] = -4(4y + -3) + -1[9(y + -1) + -18y + 4]

Combine like terms: 4y + -2y = 2y
46 + -1[-1 + 2y] = -4(4y + -3) + -1[9(y + -1) + -18y + 4]
46 + [-1 * -1 + 2y * -1] = -4(4y + -3) + -1[9(y + -1) + -18y + 4]
46 + [1 + -2y] = -4(4y + -3) + -1[9(y + -1) + -18y + 4]

Combine like terms: 46 + 1 = 47
47 + -2y = -4(4y + -3) + -1[9(y + -1) + -18y + 4]

Reorder the terms:
47 + -2y = -4(-3 + 4y) + -1[9(y + -1) + -18y + 4]
47 + -2y = (-3 * -4 + 4y * -4) + -1[9(y + -1) + -18y + 4]
47 + -2y = (12 + -16y) + -1[9(y + -1) + -18y + 4]

Reorder the terms:
47 + -2y = 12 + -16y + -1[9(-1 + y) + -18y + 4]
47 + -2y = 12 + -16y + -1[(-1 * 9 + y * 9) + -18y + 4]
47 + -2y = 12 + -16y + -1[(-9 + 9y) + -18y + 4]

Reorder the terms:
47 + -2y = 12 + -16y + -1[-9 + 4 + 9y + -18y]

Combine like terms: -9 + 4 = -5
47 + -2y = 12 + -16y + -1[-5 + 9y + -18y]

Combine like terms: 9y + -18y = -9y
47 + -2y = 12 + -16y + -1[-5 + -9y]
47 + -2y = 12 + -16y + [-5 * -1 + -9y * -1]
47 + -2y = 12 + -16y + [5 + 9y]

Reorder the terms:
47 + -2y = 12 + 5 + -16y + 9y

Combine like terms: 12 + 5 = 17
47 + -2y = 17 + -16y + 9y

Combine like terms: -16y + 9y = -7y
47 + -2y = 17 + -7y

Solving
47 + -2y = 17 + -7y

Solving for variable 'y'.

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

Add '7y' to each side of the equation.
47 + -2y + 7y = 17 + -7y + 7y

Combine like terms: -2y + 7y = 5y
47 + 5y = 17 + -7y + 7y

Combine like terms: -7y + 7y = 0
47 + 5y = 17 + 0
47 + 5y = 17

Add '-47' to each side of the equation.
47 + -47 + 5y = 17 + -47

Combine like terms: 47 + -47 = 0
0 + 5y = 17 + -47
5y = 17 + -47

Combine like terms: 17 + -47 = -30
5y = -30

Divide each side by '5'.
y = -6

Simplifying
y = -6

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