Solve d(Q):P=-6Q+27

$$d ( Q ) : P = - 6 Q + 27$$

Solve for P

$$\left\{\begin{matrix}P=-\frac{Qd}{3\left(2Q-9\right)}\text{, }&Q\neq 0\text{ and }d\neq 0\text{ and }Q\neq \frac{9}{2}\\P\neq 0\text{, }&d=0\text{ and }Q=\frac{9}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable P cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by P.

$$dQ=-6QP+P\times 27$$

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

$$-6QP+P\times 27=dQ$$

Combine all terms containing P.

$$\left(-6Q+27\right)P=dQ$$

The equation is in standard form.

$$\left(27-6Q\right)P=Qd$$

Divide both sides by -6Q+27.

$$\frac{\left(27-6Q\right)P}{27-6Q}=\frac{Qd}{27-6Q}$$

Dividing by -6Q+27 undoes the multiplication by -6Q+27.

$$P=\frac{Qd}{27-6Q}$$

Divide dQ by -6Q+27.

$$P=\frac{Qd}{3\left(9-2Q\right)}$$

Variable P cannot be equal to 0.

$$P=\frac{Qd}{3\left(9-2Q\right)}\text{, }P\neq 0$$

Solve for Q

$$Q=\frac{27P}{6P+d}$$

$$d\neq -6P\text{ and }P\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by P.

$$dQ=-6QP+P\times 27$$

Add 6QP to both sides.

$$dQ+6QP=P\times 27$$

Combine all terms containing Q.

$$\left(d+6P\right)Q=P\times 27$$

The equation is in standard form.

$$\left(6P+d\right)Q=27P$$

Divide both sides by d+6P.

$$\frac{\left(6P+d\right)Q}{6P+d}=\frac{27P}{6P+d}$$

Dividing by d+6P undoes the multiplication by d+6P.

$$Q=\frac{27P}{6P+d}$$