Solve 3x+2=(4x-2)ax

$$3 x + 2 = ( 4 x - 2 ) a x$$

Solve for a

$$a=\frac{3x+2}{2x\left(2x-1\right)}$$

$$x\neq \frac{1}{2}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4x-2 by a.

$$3x+2=\left(4xa-2a\right)x$$

Use the distributive property to multiply 4xa-2a by x.

$$3x+2=4ax^{2}-2ax$$

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

$$4ax^{2}-2ax=3x+2$$

Combine all terms containing a.

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

Divide both sides by 4x^{2}-2x.

$$\frac{\left(4x^{2}-2x\right)a}{4x^{2}-2x}=\frac{3x+2}{4x^{2}-2x}$$

Dividing by 4x^{2}-2x undoes the multiplication by 4x^{2}-2x.

$$a=\frac{3x+2}{4x^{2}-2x}$$

Divide 3x+2 by 4x^{2}-2x.

$$a=\frac{3x+2}{2x\left(2x-1\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{4a^{2}+44a+9}-2a-3}{8a}\text{; }x=\frac{\sqrt{4a^{2}+44a+9}+2a+3}{8a}\text{, }&a\neq 0\\x=-\frac{2}{3}\text{, }&a=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{4a^{2}+44a+9}-2a-3}{8a}\text{; }x=\frac{\sqrt{4a^{2}+44a+9}+2a+3}{8a}\text{, }&a\leq -2\sqrt{7}-\frac{11}{2}\text{ or }\left(a\neq 0\text{ and }a\geq 2\sqrt{7}-\frac{11}{2}\right)\\x=-\frac{2}{3}\text{, }&a=0\end{matrix}\right.$$