Solve 36-[3+8y-3(y+5)]=-3(4y-5)-[6(y-1)-5y+5]

$$36 - [ 3 + 8 y - 3 ( y + 5 ) ] = - 3 ( 4 y - 5 ) - [ 6 ( y - 1 ) - 5 y + 5 ]$$

Solve for y

$$y=-4$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by y+5.

$$36-\left(3+8y-3y-15\right)=-3\left(4y-5\right)-\left(6\left(y-1\right)-5y+5\right)$$

Combine 8y and -3y to get 5y.

$$36-\left(3+5y-15\right)=-3\left(4y-5\right)-\left(6\left(y-1\right)-5y+5\right)$$

Subtract 15 from 3 to get -12.

$$36-\left(-12+5y\right)=-3\left(4y-5\right)-\left(6\left(y-1\right)-5y+5\right)$$

To find the opposite of -12+5y, find the opposite of each term.

$$36-\left(-12\right)-5y=-3\left(4y-5\right)-\left(6\left(y-1\right)-5y+5\right)$$

The opposite of -12 is 12.

$$36+12-5y=-3\left(4y-5\right)-\left(6\left(y-1\right)-5y+5\right)$$

Add 36 and 12 to get 48.

$$48-5y=-3\left(4y-5\right)-\left(6\left(y-1\right)-5y+5\right)$$

Use the distributive property to multiply -3 by 4y-5.

$$48-5y=-12y+15-\left(6\left(y-1\right)-5y+5\right)$$

Use the distributive property to multiply 6 by y-1.

$$48-5y=-12y+15-\left(6y-6-5y+5\right)$$

Combine 6y and -5y to get y.

$$48-5y=-12y+15-\left(y-6+5\right)$$

Add -6 and 5 to get -1.

$$48-5y=-12y+15-\left(y-1\right)$$

To find the opposite of y-1, find the opposite of each term.

$$48-5y=-12y+15-y-\left(-1\right)$$

The opposite of -1 is 1.

$$48-5y=-12y+15-y+1$$

Combine -12y and -y to get -13y.

$$48-5y=-13y+15+1$$

Add 15 and 1 to get 16.

$$48-5y=-13y+16$$

Add 13y to both sides.

$$48-5y+13y=16$$

Combine -5y and 13y to get 8y.

$$48+8y=16$$

Subtract 48 from both sides.

$$8y=16-48$$

Subtract 48 from 16 to get -32.

$$8y=-32$$

Divide both sides by 8.

$$y=\frac{-32}{8}$$

Divide -32 by 8 to get -4.

$$y=-4$$