Solve 0.12aT0.04(20-a)=20*0.09

$$0.12 a T 0.04 ( 20 - a ) = 20 \times 0.09$$

Solve for T_0

$$T_{0}=-\frac{375}{a\left(a-20\right)}$$

$$a\neq 20\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply 0.12 and 0.04 to get 0.0048.

$$0.0048aT_{0}\left(20-a\right)=20\times 0.09$$

Use the distributive property to multiply 0.0048aT_{0} by 20-a.

$$0.096aT_{0}-0.0048a^{2}T_{0}=20\times 0.09$$

Multiply 20 and 0.09 to get 1.8.

$$0.096aT_{0}-0.0048a^{2}T_{0}=1.8$$

Combine all terms containing T_{0}.

$$\left(0.096a-0.0048a^{2}\right)T_{0}=1.8$$

The equation is in standard form.

$$\left(-\frac{3a^{2}}{625}+\frac{12a}{125}\right)T_{0}=1.8$$

Divide both sides by 0.096a-0.0048a^{2}.

$$\frac{\left(-\frac{3a^{2}}{625}+\frac{12a}{125}\right)T_{0}}{-\frac{3a^{2}}{625}+\frac{12a}{125}}=\frac{1.8}{-\frac{3a^{2}}{625}+\frac{12a}{125}}$$

Dividing by 0.096a-0.0048a^{2} undoes the multiplication by 0.096a-0.0048a^{2}.

$$T_{0}=\frac{1.8}{-\frac{3a^{2}}{625}+\frac{12a}{125}}$$

Divide 1.8 by 0.096a-0.0048a^{2}.

$$T_{0}=\frac{9}{5a\left(-\frac{3a}{625}+0.096\right)}$$

Solve for a

$$a=-\frac{5\left(\sqrt{T_{0}\left(4T_{0}-15\right)}-2T_{0}\right)}{T_{0}}$$

$$a=\frac{5\left(\sqrt{T_{0}\left(4T_{0}-15\right)}+2T_{0}\right)}{T_{0}}\text{, }T_{0}<0\text{ or }T_{0}\geq \frac{15}{4}$$