3(y-4)+4(y+8)=10-5(y-3)

Solution for 3(y-4)+4(y+8)=10-5(y-3) equation:

Simplifying
3(y + -4) + 4(y + 8) = 10 + -5(y + -3)

Reorder the terms:
3(-4 + y) + 4(y + 8) = 10 + -5(y + -3)
(-4 * 3 + y * 3) + 4(y + 8) = 10 + -5(y + -3)
(-12 + 3y) + 4(y + 8) = 10 + -5(y + -3)

Reorder the terms:
-12 + 3y + 4(8 + y) = 10 + -5(y + -3)
-12 + 3y + (8 * 4 + y * 4) = 10 + -5(y + -3)
-12 + 3y + (32 + 4y) = 10 + -5(y + -3)

Reorder the terms:
-12 + 32 + 3y + 4y = 10 + -5(y + -3)

Combine like terms: -12 + 32 = 20
20 + 3y + 4y = 10 + -5(y + -3)

Combine like terms: 3y + 4y = 7y
20 + 7y = 10 + -5(y + -3)

Reorder the terms:
20 + 7y = 10 + -5(-3 + y)
20 + 7y = 10 + (-3 * -5 + y * -5)
20 + 7y = 10 + (15 + -5y)

Combine like terms: 10 + 15 = 25
20 + 7y = 25 + -5y

Solving
20 + 7y = 25 + -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.
20 + 7y + 5y = 25 + -5y + 5y

Combine like terms: 7y + 5y = 12y
20 + 12y = 25 + -5y + 5y

Combine like terms: -5y + 5y = 0
20 + 12y = 25 + 0
20 + 12y = 25

Add '-20' to each side of the equation.
20 + -20 + 12y = 25 + -20

Combine like terms: 20 + -20 = 0
0 + 12y = 25 + -20
12y = 25 + -20

Combine like terms: 25 + -20 = 5
12y = 5

Divide each side by '12'.
y = 0.4166666667

Simplifying
y = 0.4166666667