Solve (y-6)(a-c)/-2b=x

$$\frac { ( y - 6 ) ( a - c ) } { - 2 b } = x$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{2bx-cy+6c}{y-6}\text{, }&y\neq 6\text{ and }b\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=6\text{ and }b\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -2b.

$$\left(y-6\right)\left(a-c\right)=x\left(-2\right)b$$

Use the distributive property to multiply y-6 by a-c.

$$ya-yc-6a+6c=x\left(-2\right)b$$

Add yc to both sides.

$$ya-6a+6c=x\left(-2\right)b+yc$$

Subtract 6c from both sides.

$$ya-6a=x\left(-2\right)b+yc-6c$$

Combine all terms containing a.

$$\left(y-6\right)a=x\left(-2\right)b+yc-6c$$

The equation is in standard form.

$$\left(y-6\right)a=-2bx+cy-6c$$

Divide both sides by y-6.

$$\frac{\left(y-6\right)a}{y-6}=\frac{-2bx+cy-6c}{y-6}$$

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

$$a=\frac{-2bx+cy-6c}{y-6}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{\left(6-y\right)\left(a-c\right)}{2x}\text{, }&a\neq c\text{ and }y\neq 6\text{ and }x\neq 0\\b\neq 0\text{, }&\left(y=6\text{ or }a=c\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by -2b.

$$\left(y-6\right)\left(a-c\right)=x\left(-2\right)b$$

Use the distributive property to multiply y-6 by a-c.

$$ya-yc-6a+6c=x\left(-2\right)b$$

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

$$x\left(-2\right)b=ya-yc-6a+6c$$

The equation is in standard form.

$$\left(-2x\right)b=ay-cy+6c-6a$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)b}{-2x}=\frac{\left(y-6\right)\left(a-c\right)}{-2x}$$

Dividing by -2x undoes the multiplication by -2x.

$$b=\frac{\left(y-6\right)\left(a-c\right)}{-2x}$$

Divide \left(-6+y\right)\left(a-c\right) by -2x.

$$b=-\frac{\left(y-6\right)\left(a-c\right)}{2x}$$

Variable b cannot be equal to 0.

$$b=-\frac{\left(y-6\right)\left(a-c\right)}{2x}\text{, }b\neq 0$$