Solve c(x-a)+d(x-h)=0

$$c ( x - a ) + d ( x - h ) = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{cx+dx-dh}{c}\text{, }&c\neq 0\\a\in \mathrm{C}\text{, }&\left(d=0\text{ or }x=h\right)\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$cx-ca+d\left(x-h\right)=0$$

Use the distributive property to multiply d by x-h.

$$cx-ca+dx-dh=0$$

Subtract cx from both sides. Anything subtracted from zero gives its negation.

$$-ca+dx-dh=-cx$$

Subtract dx from both sides.

$$-ca-dh=-cx-dx$$

Add dh to both sides.

$$-ca=-cx-dx+dh$$

Reorder the terms.

$$-ac=-cx-dx+dh$$

The equation is in standard form.

$$\left(-c\right)a=dh-dx-cx$$

Divide both sides by -c.

$$\frac{\left(-c\right)a}{-c}=\frac{dh-dx-cx}{-c}$$

Dividing by -c undoes the multiplication by -c.

$$a=\frac{dh-dx-cx}{-c}$$

Divide -xc-dx+dh by -c.

$$a=\frac{dx-dh}{c}+x$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=-\frac{d\left(x-h\right)}{x-a}\text{, }&x\neq a\\c\in \mathrm{C}\text{, }&\left(d=0\text{ and }x=a\right)\text{ or }\left(x=h\text{ and }a=h\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$cx-ca+d\left(x-h\right)=0$$

Use the distributive property to multiply d by x-h.

$$cx-ca+dx-dh=0$$

Subtract dx from both sides. Anything subtracted from zero gives its negation.

$$cx-ca-dh=-dx$$

Add dh to both sides.

$$cx-ca=-dx+dh$$

Reorder the terms.

$$cx-ac=-dx+dh$$

Combine all terms containing c.

$$\left(x-a\right)c=-dx+dh$$

The equation is in standard form.

$$\left(x-a\right)c=dh-dx$$

Divide both sides by x-a.

$$\frac{\left(x-a\right)c}{x-a}=\frac{d\left(h-x\right)}{x-a}$$

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

$$c=\frac{d\left(h-x\right)}{x-a}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{cx+dx-dh}{c}\text{, }&c\neq 0\\a\in \mathrm{R}\text{, }&\left(d=0\text{ or }x=h\right)\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$cx-ca+d\left(x-h\right)=0$$

Use the distributive property to multiply d by x-h.

$$cx-ca+dx-dh=0$$

Subtract cx from both sides. Anything subtracted from zero gives its negation.

$$-ca+dx-dh=-cx$$

Subtract dx from both sides.

$$-ca-dh=-cx-dx$$

Add dh to both sides.

$$-ca=-cx-dx+dh$$

Reorder the terms.

$$-ac=-cx-dx+dh$$

The equation is in standard form.

$$\left(-c\right)a=dh-dx-cx$$

Divide both sides by -c.

$$\frac{\left(-c\right)a}{-c}=\frac{dh-dx-cx}{-c}$$

Dividing by -c undoes the multiplication by -c.

$$a=\frac{dh-dx-cx}{-c}$$

Divide -cx-dx+dh by -c.

$$a=\frac{dx-dh}{c}+x$$

Solve for c

$$\left\{\begin{matrix}c=-\frac{d\left(x-h\right)}{x-a}\text{, }&x\neq a\\c\in \mathrm{R}\text{, }&\left(d=0\text{ and }x=a\right)\text{ or }\left(x=h\text{ and }a=h\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$cx-ca+d\left(x-h\right)=0$$

Use the distributive property to multiply d by x-h.

$$cx-ca+dx-dh=0$$

Subtract dx from both sides. Anything subtracted from zero gives its negation.

$$cx-ca-dh=-dx$$

Add dh to both sides.

$$cx-ca=-dx+dh$$

Reorder the terms.

$$cx-ac=-dx+dh$$

Combine all terms containing c.

$$\left(x-a\right)c=-dx+dh$$

The equation is in standard form.

$$\left(x-a\right)c=dh-dx$$

Divide both sides by x-a.

$$\frac{\left(x-a\right)c}{x-a}=\frac{d\left(h-x\right)}{x-a}$$

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

$$c=\frac{d\left(h-x\right)}{x-a}$$