4(y+5)-6(2y+3)=3(y+14)-2(5-y)+9

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Solution for 4(y+5)-6(2y+3)=3(y+14)-2(5-y)+9 equation: 


Simplifying
4(y + 5) + -6(2y + 3) = 3(y + 14) + -2(5 + -1y) + 9

Reorder the terms:
4(5 + y) + -6(2y + 3) = 3(y + 14) + -2(5 + -1y) + 9
(5 * 4 + y * 4) + -6(2y + 3) = 3(y + 14) + -2(5 + -1y) + 9
(20 + 4y) + -6(2y + 3) = 3(y + 14) + -2(5 + -1y) + 9

Reorder the terms:
20 + 4y + -6(3 + 2y) = 3(y + 14) + -2(5 + -1y) + 9
20 + 4y + (3 * -6 + 2y * -6) = 3(y + 14) + -2(5 + -1y) + 9
20 + 4y + (-18 + -12y) = 3(y + 14) + -2(5 + -1y) + 9

Reorder the terms:
20 + -18 + 4y + -12y = 3(y + 14) + -2(5 + -1y) + 9

Combine like terms: 20 + -18 = 2
2 + 4y + -12y = 3(y + 14) + -2(5 + -1y) + 9

Combine like terms: 4y + -12y = -8y
2 + -8y = 3(y + 14) + -2(5 + -1y) + 9

Reorder the terms:
2 + -8y = 3(14 + y) + -2(5 + -1y) + 9
2 + -8y = (14 * 3 + y * 3) + -2(5 + -1y) + 9
2 + -8y = (42 + 3y) + -2(5 + -1y) + 9
2 + -8y = 42 + 3y + (5 * -2 + -1y * -2) + 9
2 + -8y = 42 + 3y + (-10 + 2y) + 9

Reorder the terms:
2 + -8y = 42 + -10 + 9 + 3y + 2y

Combine like terms: 42 + -10 = 32
2 + -8y = 32 + 9 + 3y + 2y

Combine like terms: 32 + 9 = 41
2 + -8y = 41 + 3y + 2y

Combine like terms: 3y + 2y = 5y
2 + -8y = 41 + 5y

Solving
2 + -8y = 41 + 5y

Solving for variable 'y'.

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

Add '-5y' to each side of the equation.
2 + -8y + -5y = 41 + 5y + -5y

Combine like terms: -8y + -5y = -13y
2 + -13y = 41 + 5y + -5y

Combine like terms: 5y + -5y = 0
2 + -13y = 41 + 0
2 + -13y = 41

Add '-2' to each side of the equation.
2 + -2 + -13y = 41 + -2

Combine like terms: 2 + -2 = 0
0 + -13y = 41 + -2
-13y = 41 + -2

Combine like terms: 41 + -2 = 39
-13y = 39

Divide each side by '-13'.
y = -3

Simplifying
y = -3

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