Solve 6(b-x)=c(c-x)

$$6 ( b - x ) = c ( c - x )$$

Solve for b

$$b=-\frac{cx}{6}+\frac{c^{2}}{6}+x$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by b-x.

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

Use the distributive property to multiply c by c-x.

$$6b-6x=c^{2}-cx$$

Add 6x to both sides.

$$6b=c^{2}-cx+6x$$

The equation is in standard form.

$$6b=c^{2}+6x-cx$$

Divide both sides by 6.

$$\frac{6b}{6}=\frac{c^{2}+6x-cx}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$b=\frac{c^{2}+6x-cx}{6}$$

Divide c^{2}-cx+6x by 6.

$$b=-\frac{cx}{6}+\frac{c^{2}}{6}+x$$

Solve for c (complex solution)

$$c=\frac{-\sqrt{x^{2}-24x+24b}+x}{2}$$

$$c=\frac{\sqrt{x^{2}-24x+24b}+x}{2}$$

Solve for c

$$c=\frac{-\sqrt{x^{2}-24x+24b}+x}{2}$$

$$c=\frac{\sqrt{x^{2}-24x+24b}+x}{2}\text{, }b\geq -\frac{x^{2}}{24}+x$$