30-[3+6y-2(y+2)]=-5(4y-7)-[9(y-1)-22y+31]

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Solution for 30-[3+6y-2(y+2)]=-5(4y-7)-[9(y-1)-22y+31] equation:


Simplifying
30 + -1[3 + 6y + -2(y + 2)] = -5(4y + -7) + -1[9(y + -1) + -22y + 31]

Reorder the terms:
30 + -1[3 + 6y + -2(2 + y)] = -5(4y + -7) + -1[9(y + -1) + -22y + 31]
30 + -1[3 + 6y + (2 * -2 + y * -2)] = -5(4y + -7) + -1[9(y + -1) + -22y + 31]
30 + -1[3 + 6y + (-4 + -2y)] = -5(4y + -7) + -1[9(y + -1) + -22y + 31]

Reorder the terms:
30 + -1[3 + -4 + 6y + -2y] = -5(4y + -7) + -1[9(y + -1) + -22y + 31]

Combine like terms: 3 + -4 = -1
30 + -1[-1 + 6y + -2y] = -5(4y + -7) + -1[9(y + -1) + -22y + 31]

Combine like terms: 6y + -2y = 4y
30 + -1[-1 + 4y] = -5(4y + -7) + -1[9(y + -1) + -22y + 31]
30 + [-1 * -1 + 4y * -1] = -5(4y + -7) + -1[9(y + -1) + -22y + 31]
30 + [1 + -4y] = -5(4y + -7) + -1[9(y + -1) + -22y + 31]

Combine like terms: 30 + 1 = 31
31 + -4y = -5(4y + -7) + -1[9(y + -1) + -22y + 31]

Reorder the terms:
31 + -4y = -5(-7 + 4y) + -1[9(y + -1) + -22y + 31]
31 + -4y = (-7 * -5 + 4y * -5) + -1[9(y + -1) + -22y + 31]
31 + -4y = (35 + -20y) + -1[9(y + -1) + -22y + 31]

Reorder the terms:
31 + -4y = 35 + -20y + -1[9(-1 + y) + -22y + 31]
31 + -4y = 35 + -20y + -1[(-1 * 9 + y * 9) + -22y + 31]
31 + -4y = 35 + -20y + -1[(-9 + 9y) + -22y + 31]

Reorder the terms:
31 + -4y = 35 + -20y + -1[-9 + 31 + 9y + -22y]

Combine like terms: -9 + 31 = 22
31 + -4y = 35 + -20y + -1[22 + 9y + -22y]

Combine like terms: 9y + -22y = -13y
31 + -4y = 35 + -20y + -1[22 + -13y]
31 + -4y = 35 + -20y + [22 * -1 + -13y * -1]
31 + -4y = 35 + -20y + [-22 + 13y]

Reorder the terms:
31 + -4y = 35 + -22 + -20y + 13y

Combine like terms: 35 + -22 = 13
31 + -4y = 13 + -20y + 13y

Combine like terms: -20y + 13y = -7y
31 + -4y = 13 + -7y

Solving
31 + -4y = 13 + -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.
31 + -4y + 7y = 13 + -7y + 7y

Combine like terms: -4y + 7y = 3y
31 + 3y = 13 + -7y + 7y

Combine like terms: -7y + 7y = 0
31 + 3y = 13 + 0
31 + 3y = 13

Add '-31' to each side of the equation.
31 + -31 + 3y = 13 + -31

Combine like terms: 31 + -31 = 0
0 + 3y = 13 + -31
3y = 13 + -31

Combine like terms: 13 + -31 = -18
3y = -18

Divide each side by '3'.
y = -6

Simplifying
y = -6

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