Solve 3(2a-x)+ax=a^2+9

$$3 ( 2 a - x ) + a x = a ^ { 2 } + 9$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=a-3\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2a-x.

$$6a-3x+ax=a^{2}+9$$

Subtract 6a from both sides.

$$-3x+ax=a^{2}+9-6a$$

Combine all terms containing x.

$$\left(-3+a\right)x=a^{2}+9-6a$$

The equation is in standard form.

$$\left(a-3\right)x=a^{2}-6a+9$$

Divide both sides by -3+a.

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

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

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

Divide \left(a-3\right)^{2} by -3+a.

$$x=a-3$$

Solve for x

$$\left\{\begin{matrix}\\x=a-3\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&a=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2a-x.

$$6a-3x+ax=a^{2}+9$$

Subtract 6a from both sides.

$$-3x+ax=a^{2}+9-6a$$

Combine all terms containing x.

$$\left(-3+a\right)x=a^{2}+9-6a$$

The equation is in standard form.

$$\left(a-3\right)x=a^{2}-6a+9$$

Divide both sides by -3+a.

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

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

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

Divide \left(a-3\right)^{2} by -3+a.

$$x=a-3$$

Solve for a

$$a=3$$

$$a=x+3$$