6y+3(4-y)=8-2(y+3)

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Solution for 6y+3(4-y)=8-2(y+3) equation: 


Simplifying
6y + 3(4 + -1y) = 8 + -2(y + 3)
6y + (4 * 3 + -1y * 3) = 8 + -2(y + 3)
6y + (12 + -3y) = 8 + -2(y + 3)

Reorder the terms:
12 + 6y + -3y = 8 + -2(y + 3)

Combine like terms: 6y + -3y = 3y
12 + 3y = 8 + -2(y + 3)

Reorder the terms:
12 + 3y = 8 + -2(3 + y)
12 + 3y = 8 + (3 * -2 + y * -2)
12 + 3y = 8 + (-6 + -2y)

Combine like terms: 8 + -6 = 2
12 + 3y = 2 + -2y

Solving
12 + 3y = 2 + -2y

Solving for variable 'y'.

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

Add '2y' to each side of the equation.
12 + 3y + 2y = 2 + -2y + 2y

Combine like terms: 3y + 2y = 5y
12 + 5y = 2 + -2y + 2y

Combine like terms: -2y + 2y = 0
12 + 5y = 2 + 0
12 + 5y = 2

Add '-12' to each side of the equation.
12 + -12 + 5y = 2 + -12

Combine like terms: 12 + -12 = 0
0 + 5y = 2 + -12
5y = 2 + -12

Combine like terms: 2 + -12 = -10
5y = -10

Divide each side by '5'.
y = -2

Simplifying
y = -2

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