Solve ax+x(3-2a)-6a=0

$$a x + x ( 3 - 2 a ) - 6 a = 0$$

Solve for a

$$a=\frac{3x}{x+6}$$

$$x\neq -6$$

Steps for Solving Linear Equation

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

$$ax+3x-2xa-6a=0$$

Combine ax and -2xa to get -ax.

$$-ax+3x-6a=0$$

Subtract 3x from both sides. Anything subtracted from zero gives its negation.

$$-ax-6a=-3x$$

Combine all terms containing a.

$$\left(-x-6\right)a=-3x$$

Divide both sides by -x-6.

$$\frac{\left(-x-6\right)a}{-x-6}=-\frac{3x}{-x-6}$$

Dividing by -x-6 undoes the multiplication by -x-6.

$$a=-\frac{3x}{-x-6}$$

Divide -3x by -x-6.

$$a=\frac{3x}{x+6}$$

Solve for x

$$x=\frac{6a}{3-a}$$

$$a\neq 3$$

Steps for Solving Linear Equation

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

$$ax+3x-2xa-6a=0$$

Combine ax and -2xa to get -ax.

$$-ax+3x-6a=0$$

Add 6a to both sides. Anything plus zero gives itself.

$$-ax+3x=6a$$

Combine all terms containing x.

$$\left(-a+3\right)x=6a$$

The equation is in standard form.

$$\left(3-a\right)x=6a$$

Divide both sides by 3-a.

$$\frac{\left(3-a\right)x}{3-a}=\frac{6a}{3-a}$$

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

$$x=\frac{6a}{3-a}$$