43-[3+6y-3(y+5)]=-3(2y-6)-[9(y-1)-6y+8]

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Solution for 43-[3+6y-3(y+5)]=-3(2y-6)-[9(y-1)-6y+8] equation:


Simplifying
43 + -1[3 + 6y + -3(y + 5)] = -3(2y + -6) + -1[9(y + -1) + -6y + 8]

Reorder the terms:
43 + -1[3 + 6y + -3(5 + y)] = -3(2y + -6) + -1[9(y + -1) + -6y + 8]
43 + -1[3 + 6y + (5 * -3 + y * -3)] = -3(2y + -6) + -1[9(y + -1) + -6y + 8]
43 + -1[3 + 6y + (-15 + -3y)] = -3(2y + -6) + -1[9(y + -1) + -6y + 8]

Reorder the terms:
43 + -1[3 + -15 + 6y + -3y] = -3(2y + -6) + -1[9(y + -1) + -6y + 8]

Combine like terms: 3 + -15 = -12
43 + -1[-12 + 6y + -3y] = -3(2y + -6) + -1[9(y + -1) + -6y + 8]

Combine like terms: 6y + -3y = 3y
43 + -1[-12 + 3y] = -3(2y + -6) + -1[9(y + -1) + -6y + 8]
43 + [-12 * -1 + 3y * -1] = -3(2y + -6) + -1[9(y + -1) + -6y + 8]
43 + [12 + -3y] = -3(2y + -6) + -1[9(y + -1) + -6y + 8]

Combine like terms: 43 + 12 = 55
55 + -3y = -3(2y + -6) + -1[9(y + -1) + -6y + 8]

Reorder the terms:
55 + -3y = -3(-6 + 2y) + -1[9(y + -1) + -6y + 8]
55 + -3y = (-6 * -3 + 2y * -3) + -1[9(y + -1) + -6y + 8]
55 + -3y = (18 + -6y) + -1[9(y + -1) + -6y + 8]

Reorder the terms:
55 + -3y = 18 + -6y + -1[9(-1 + y) + -6y + 8]
55 + -3y = 18 + -6y + -1[(-1 * 9 + y * 9) + -6y + 8]
55 + -3y = 18 + -6y + -1[(-9 + 9y) + -6y + 8]

Reorder the terms:
55 + -3y = 18 + -6y + -1[-9 + 8 + 9y + -6y]

Combine like terms: -9 + 8 = -1
55 + -3y = 18 + -6y + -1[-1 + 9y + -6y]

Combine like terms: 9y + -6y = 3y
55 + -3y = 18 + -6y + -1[-1 + 3y]
55 + -3y = 18 + -6y + [-1 * -1 + 3y * -1]
55 + -3y = 18 + -6y + [1 + -3y]

Reorder the terms:
55 + -3y = 18 + 1 + -6y + -3y

Combine like terms: 18 + 1 = 19
55 + -3y = 19 + -6y + -3y

Combine like terms: -6y + -3y = -9y
55 + -3y = 19 + -9y

Solving
55 + -3y = 19 + -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.
55 + -3y + 9y = 19 + -9y + 9y

Combine like terms: -3y + 9y = 6y
55 + 6y = 19 + -9y + 9y

Combine like terms: -9y + 9y = 0
55 + 6y = 19 + 0
55 + 6y = 19

Add '-55' to each side of the equation.
55 + -55 + 6y = 19 + -55

Combine like terms: 55 + -55 = 0
0 + 6y = 19 + -55
6y = 19 + -55

Combine like terms: 19 + -55 = -36
6y = -36

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

Simplifying
y = -6

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