Solve 4x^4a-108xa=4xa(x^2+3x+9)

$$4 x ^ { 4 } a - 108 x a = 4 x a ( x ^ { 2 } + 3 x + 9 )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=\frac{-3+3\sqrt{3}i}{2}\text{ or }x=\frac{-3\sqrt{3}i-3}{2}\text{ or }x=4\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4xa by x^{2}+3x+9.

$$4x^{4}a-108xa=4ax^{3}+12ax^{2}+36ax$$

Subtract 4ax^{3} from both sides.

$$4x^{4}a-108xa-4ax^{3}=12ax^{2}+36ax$$

Subtract 12ax^{2} from both sides.

$$4x^{4}a-108xa-4ax^{3}-12ax^{2}=36ax$$

Subtract 36ax from both sides.

$$4x^{4}a-108xa-4ax^{3}-12ax^{2}-36ax=0$$

Combine -108xa and -36ax to get -144xa.

$$4x^{4}a-144xa-4ax^{3}-12ax^{2}=0$$

Combine all terms containing a.

$$\left(4x^{4}-144x-4x^{3}-12x^{2}\right)a=0$$

The equation is in standard form.

$$\left(4x^{4}-4x^{3}-12x^{2}-144x\right)a=0$$

Divide 0 by 4x^{4}-144x-4x^{3}-12x^{2}.

$$a=0$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=4\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4xa by x^{2}+3x+9.

$$4x^{4}a-108xa=4ax^{3}+12ax^{2}+36ax$$

Subtract 4ax^{3} from both sides.

$$4x^{4}a-108xa-4ax^{3}=12ax^{2}+36ax$$

Subtract 12ax^{2} from both sides.

$$4x^{4}a-108xa-4ax^{3}-12ax^{2}=36ax$$

Subtract 36ax from both sides.

$$4x^{4}a-108xa-4ax^{3}-12ax^{2}-36ax=0$$

Combine -108xa and -36ax to get -144xa.

$$4x^{4}a-144xa-4ax^{3}-12ax^{2}=0$$

Combine all terms containing a.

$$\left(4x^{4}-144x-4x^{3}-12x^{2}\right)a=0$$

The equation is in standard form.

$$\left(4x^{4}-4x^{3}-12x^{2}-144x\right)a=0$$

Divide 0 by 4x^{4}-144x-4x^{3}-12x^{2}.

$$a=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=4\text{; }x=0\text{; }x=\frac{-3\sqrt{3}i-3}{2}\text{; }x=\frac{-3+3\sqrt{3}i}{2}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=4\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$