Solve -1=(3-p)(3-q)

$$- 1 = ( 3 - p ) ( 3 - q )$$

Solve for p

$$p=-\frac{3q-10}{3-q}$$

$$q\neq 3$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3-p by 3-q.

$$-1=9-3q-3p+pq$$

Swap sides so that all variable terms are on the left hand side.

$$9-3q-3p+pq=-1$$

Subtract 9 from both sides.

$$-3q-3p+pq=-1-9$$

Subtract 9 from -1 to get -10.

$$-3q-3p+pq=-10$$

Add 3q to both sides.

$$-3p+pq=-10+3q$$

Combine all terms containing p.

$$\left(-3+q\right)p=-10+3q$$

The equation is in standard form.

$$\left(q-3\right)p=3q-10$$

Divide both sides by -3+q.

$$\frac{\left(q-3\right)p}{q-3}=\frac{3q-10}{q-3}$$

Dividing by -3+q undoes the multiplication by -3+q.

$$p=\frac{3q-10}{q-3}$$

Solve for q

$$q=-\frac{3p-10}{3-p}$$

$$p\neq 3$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3-p by 3-q.

$$-1=9-3q-3p+pq$$

Swap sides so that all variable terms are on the left hand side.

$$9-3q-3p+pq=-1$$

Subtract 9 from both sides.

$$-3q-3p+pq=-1-9$$

Subtract 9 from -1 to get -10.

$$-3q-3p+pq=-10$$

Add 3p to both sides.

$$-3q+pq=-10+3p$$

Combine all terms containing q.

$$\left(-3+p\right)q=-10+3p$$

The equation is in standard form.

$$\left(p-3\right)q=3p-10$$

Divide both sides by -3+p.

$$\frac{\left(p-3\right)q}{p-3}=\frac{3p-10}{p-3}$$

Dividing by -3+p undoes the multiplication by -3+p.

$$q=\frac{3p-10}{p-3}$$