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

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


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

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

Reorder the terms:
-12 + 3y + 5(2 + y) = 4(y + -3)
-12 + 3y + (2 * 5 + y * 5) = 4(y + -3)
-12 + 3y + (10 + 5y) = 4(y + -3)

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

Combine like terms: -12 + 10 = -2
-2 + 3y + 5y = 4(y + -3)

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

Reorder the terms:
-2 + 8y = 4(-3 + y)
-2 + 8y = (-3 * 4 + y * 4)
-2 + 8y = (-12 + 4y)

Solving
-2 + 8y = -12 + 4y

Solving for variable 'y'.

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

Add '-4y' to each side of the equation.
-2 + 8y + -4y = -12 + 4y + -4y

Combine like terms: 8y + -4y = 4y
-2 + 4y = -12 + 4y + -4y

Combine like terms: 4y + -4y = 0
-2 + 4y = -12 + 0
-2 + 4y = -12

Add '2' to each side of the equation.
-2 + 2 + 4y = -12 + 2

Combine like terms: -2 + 2 = 0
0 + 4y = -12 + 2
4y = -12 + 2

Combine like terms: -12 + 2 = -10
4y = -10

Divide each side by '4'.
y = -2.5

Simplifying
y = -2.5

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