Solve y/2*left(2*34+4left(y-1right)right)>0

$$\frac{ y }{ 2 } \times \left( 2 \times 34+4 \left( y-1 \right) \right) > 0$$

Solve for y

$$y\in \left(-\infty,-16\right)\cup \left(0,\infty\right)$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$y\left(2\times 34+4\left(y-1\right)\right)>0$$

Multiply 2 and 34 to get 68.

$$y\left(68+4\left(y-1\right)\right)>0$$

Use the distributive property to multiply 4 by y-1.

$$y\left(68+4y-4\right)>0$$

Subtract 4 from 68 to get 64.

$$y\left(64+4y\right)>0$$

Use the distributive property to multiply y by 64+4y.

$$64y+4y^{2}>0$$

Factor out y.

$$4y\left(y+16\right)>0$$

For the product to be positive, y+16 and y have to be both negative or both positive. Consider the case when y+16 and y are both negative.

$$y+16<0 y<0$$

The solution satisfying both inequalities is y<-16.

$$y<-16$$

Consider the case when y+16 and y are both positive.

$$y>0 y+16>0$$

The solution satisfying both inequalities is y>0.

$$y>0$$

The final solution is the union of the obtained solutions.

$$y<-16\text{; }y>0$$