2(y-1)-3(y-2)+4(y-3)=2(y+5)

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Solution for 2(y-1)-3(y-2)+4(y-3)=2(y+5) equation:


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

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

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

Reorder the terms:
-2 + 2y + 6 + -3y + 4(-3 + y) = 2(y + 5)
-2 + 2y + 6 + -3y + (-3 * 4 + y * 4) = 2(y + 5)
-2 + 2y + 6 + -3y + (-12 + 4y) = 2(y + 5)

Reorder the terms:
-2 + 6 + -12 + 2y + -3y + 4y = 2(y + 5)

Combine like terms: -2 + 6 = 4
4 + -12 + 2y + -3y + 4y = 2(y + 5)

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

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

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

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

Solving
-8 + 3y = 10 + 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.
-8 + 3y + -2y = 10 + 2y + -2y

Combine like terms: 3y + -2y = 1y
-8 + 1y = 10 + 2y + -2y

Combine like terms: 2y + -2y = 0
-8 + 1y = 10 + 0
-8 + 1y = 10

Add '8' to each side of the equation.
-8 + 8 + 1y = 10 + 8

Combine like terms: -8 + 8 = 0
0 + 1y = 10 + 8
1y = 10 + 8

Combine like terms: 10 + 8 = 18
1y = 18

Divide each side by '1'.
y = 18

Simplifying
y = 18

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