Solve 9+left(a+yright)(-3y)+y+2a-4=0

$$9+ \left( a+y \right) (-3y)+y+2a-4 = 0$$

Solve for a

$$a=-\frac{5+y-3y^{2}}{2-3y}$$

$$y\neq \frac{2}{3}$$

Steps for Solving Linear Equation

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

$$9+\left(-3a-3y\right)y+y+2a-4=0$$

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

$$9-3ay-3y^{2}+y+2a-4=0$$

Subtract 4 from 9 to get 5.

$$5-3ay-3y^{2}+y+2a=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-3ay-3y^{2}+y+2a=-5$$

Add 3y^{2} to both sides.

$$-3ay+y+2a=-5+3y^{2}$$

Subtract y from both sides.

$$-3ay+2a=-5+3y^{2}-y$$

Combine all terms containing a.

$$\left(-3y+2\right)a=-5+3y^{2}-y$$

The equation is in standard form.

$$\left(2-3y\right)a=3y^{2}-y-5$$

Divide both sides by 2-3y.

$$\frac{\left(2-3y\right)a}{2-3y}=\frac{3y^{2}-y-5}{2-3y}$$

Dividing by 2-3y undoes the multiplication by 2-3y.

$$a=\frac{3y^{2}-y-5}{2-3y}$$

Solve for y

$$y=-\frac{\sqrt{9a^{2}+18a+61}}{6}-\frac{a}{2}+\frac{1}{6}$$

$$y=\frac{\sqrt{9a^{2}+18a+61}}{6}-\frac{a}{2}+\frac{1}{6}$$