43-[4+9y-3(y+5)]=-5(2y+3)-[6(y-1)-3y+2]

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Solution for 43-[4+9y-3(y+5)]=-5(2y+3)-[6(y-1)-3y+2] equation:


Simplifying
43 + -1[4 + 9y + -3(y + 5)] = -5(2y + 3) + -1[6(y + -1) + -3y + 2]

Reorder the terms:
43 + -1[4 + 9y + -3(5 + y)] = -5(2y + 3) + -1[6(y + -1) + -3y + 2]
43 + -1[4 + 9y + (5 * -3 + y * -3)] = -5(2y + 3) + -1[6(y + -1) + -3y + 2]
43 + -1[4 + 9y + (-15 + -3y)] = -5(2y + 3) + -1[6(y + -1) + -3y + 2]

Reorder the terms:
43 + -1[4 + -15 + 9y + -3y] = -5(2y + 3) + -1[6(y + -1) + -3y + 2]

Combine like terms: 4 + -15 = -11
43 + -1[-11 + 9y + -3y] = -5(2y + 3) + -1[6(y + -1) + -3y + 2]

Combine like terms: 9y + -3y = 6y
43 + -1[-11 + 6y] = -5(2y + 3) + -1[6(y + -1) + -3y + 2]
43 + [-11 * -1 + 6y * -1] = -5(2y + 3) + -1[6(y + -1) + -3y + 2]
43 + [11 + -6y] = -5(2y + 3) + -1[6(y + -1) + -3y + 2]

Combine like terms: 43 + 11 = 54
54 + -6y = -5(2y + 3) + -1[6(y + -1) + -3y + 2]

Reorder the terms:
54 + -6y = -5(3 + 2y) + -1[6(y + -1) + -3y + 2]
54 + -6y = (3 * -5 + 2y * -5) + -1[6(y + -1) + -3y + 2]
54 + -6y = (-15 + -10y) + -1[6(y + -1) + -3y + 2]

Reorder the terms:
54 + -6y = -15 + -10y + -1[6(-1 + y) + -3y + 2]
54 + -6y = -15 + -10y + -1[(-1 * 6 + y * 6) + -3y + 2]
54 + -6y = -15 + -10y + -1[(-6 + 6y) + -3y + 2]

Reorder the terms:
54 + -6y = -15 + -10y + -1[-6 + 2 + 6y + -3y]

Combine like terms: -6 + 2 = -4
54 + -6y = -15 + -10y + -1[-4 + 6y + -3y]

Combine like terms: 6y + -3y = 3y
54 + -6y = -15 + -10y + -1[-4 + 3y]
54 + -6y = -15 + -10y + [-4 * -1 + 3y * -1]
54 + -6y = -15 + -10y + [4 + -3y]

Reorder the terms:
54 + -6y = -15 + 4 + -10y + -3y

Combine like terms: -15 + 4 = -11
54 + -6y = -11 + -10y + -3y

Combine like terms: -10y + -3y = -13y
54 + -6y = -11 + -13y

Solving
54 + -6y = -11 + -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.
54 + -6y + 13y = -11 + -13y + 13y

Combine like terms: -6y + 13y = 7y
54 + 7y = -11 + -13y + 13y

Combine like terms: -13y + 13y = 0
54 + 7y = -11 + 0
54 + 7y = -11

Add '-54' to each side of the equation.
54 + -54 + 7y = -11 + -54

Combine like terms: 54 + -54 = 0
0 + 7y = -11 + -54
7y = -11 + -54

Combine like terms: -11 + -54 = -65
7y = -65

Divide each side by '7'.
y = -9.285714286

Simplifying
y = -9.285714286

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