Solve 3(9-y)-42=17y-5(3+4y)

$$3 ( 9 - y ) - 42 = 17 y - 5 ( 3 + 4 y )$$

Solve for y (complex solution)

$$y\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 3 by 9-y.

$$27-3y-42=17y-5\left(3+4y\right)$$

Subtract 42 from 27 to get -15.

$$-15-3y=17y-5\left(3+4y\right)$$

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

$$-15-3y=17y-15-20y$$

Combine 17y and -20y to get -3y.

$$-15-3y=-3y-15$$

Add 3y to both sides.

$$-15-3y+3y=-15$$

Combine -3y and 3y to get 0.

$$-15=-15$$

Compare -15 and -15.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{C}$$

Solve for y

$$y\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 3 by 9-y.

$$27-3y-42=17y-5\left(3+4y\right)$$

Subtract 42 from 27 to get -15.

$$-15-3y=17y-5\left(3+4y\right)$$

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

$$-15-3y=17y-15-20y$$

Combine 17y and -20y to get -3y.

$$-15-3y=-3y-15$$

Add 3y to both sides.

$$-15-3y+3y=-15$$

Combine -3y and 3y to get 0.

$$-15=-15$$

Compare -15 and -15.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{R}$$