Solve TC=450+100q-4q^2+0.2q^3

$$T C = 450 + 100 q - 4 q ^ { 2 } + 0.2 q ^ { 3 }$$

Solve for C

$$\left\{\begin{matrix}C=\frac{q^{3}-20q^{2}+500q+2250}{5T}\text{, }&T\neq 0\\C\in \mathrm{R}\text{, }&q=-\frac{1}{3}\sqrt[3]{27\times \frac{1375\sqrt{345}}{9}+67375}+\frac{\sqrt[3]{4125\sqrt{345}-67375}}{3}+\frac{20}{3}\text{ and }T=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$TC=\frac{q^{3}}{5}-4q^{2}+100q+450$$

Divide both sides by T.

$$\frac{TC}{T}=\frac{\frac{q^{3}}{5}-4q^{2}+100q+450}{T}$$

Dividing by T undoes the multiplication by T.

$$C=\frac{\frac{q^{3}}{5}-4q^{2}+100q+450}{T}$$

Divide 450+100q-4q^{2}+\frac{q^{3}}{5} by T.

$$C=\frac{q^{3}-20q^{2}+500q+2250}{5T}$$

Solve for T

$$\left\{\begin{matrix}T=\frac{q^{3}-20q^{2}+500q+2250}{5C}\text{, }&C\neq 0\\T\in \mathrm{R}\text{, }&q=-\frac{1}{3}\sqrt[3]{27\times \frac{1375\sqrt{345}}{9}+67375}+\frac{\sqrt[3]{4125\sqrt{345}-67375}}{3}+\frac{20}{3}\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$CT=\frac{q^{3}}{5}-4q^{2}+100q+450$$

Divide both sides by C.

$$\frac{CT}{C}=\frac{\frac{q^{3}}{5}-4q^{2}+100q+450}{C}$$

Dividing by C undoes the multiplication by C.

$$T=\frac{\frac{q^{3}}{5}-4q^{2}+100q+450}{C}$$

Divide 450+100q-4q^{2}+\frac{q^{3}}{5} by C.

$$T=\frac{q^{3}-20q^{2}+500q+2250}{5C}$$