Solve x^2-5x+6/2ax-6a=(x-2)/20

$$\frac { x ^ { 2 } - 5 x + 6 } { 2 a x - 6 a } = \frac { ( x - 2 ) } { 20 }$$

Solve for a

$$\left\{\begin{matrix}a=10\text{, }&x\neq 3\\a\neq 0\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 20a\left(x-3\right), the least common multiple of 2ax-6a,20.

$$10\left(x^{2}-5x+6\right)=a\left(x-3\right)\left(x-2\right)$$

Use the distributive property to multiply 10 by x^{2}-5x+6.

$$10x^{2}-50x+60=a\left(x-3\right)\left(x-2\right)$$

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

$$10x^{2}-50x+60=\left(ax-3a\right)\left(x-2\right)$$

Use the distributive property to multiply ax-3a by x-2 and combine like terms.

$$10x^{2}-50x+60=ax^{2}-5ax+6a$$

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

$$ax^{2}-5ax+6a=10x^{2}-50x+60$$

Combine all terms containing a.

$$\left(x^{2}-5x+6\right)a=10x^{2}-50x+60$$

Divide both sides by x^{2}-5x+6.

$$\frac{\left(x^{2}-5x+6\right)a}{x^{2}-5x+6}=\frac{10\left(x-3\right)\left(x-2\right)}{x^{2}-5x+6}$$

Dividing by x^{2}-5x+6 undoes the multiplication by x^{2}-5x+6.

$$a=\frac{10\left(x-3\right)\left(x-2\right)}{x^{2}-5x+6}$$

Divide 10\left(-3+x\right)\left(-2+x\right) by x^{2}-5x+6.

$$a=10$$

Solve for x

$$\left\{\begin{matrix}x=2\text{, }&a\neq 0\\x\neq 3\text{, }&a=10\end{matrix}\right.$$