Solve x(x-a)-13=3(1-x)

$$x ( x - a ) - 13 = 3 ( 1 - x )$$

Solve for a

$$a=x+3-\frac{16}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$x^{2}-xa-13=3\left(1-x\right)$$

Use the distributive property to multiply 3 by 1-x.

$$x^{2}-xa-13=3-3x$$

Subtract x^{2} from both sides.

$$-xa-13=3-3x-x^{2}$$

Add 13 to both sides.

$$-xa=3-3x-x^{2}+13$$

Add 3 and 13 to get 16.

$$-xa=16-3x-x^{2}$$

The equation is in standard form.

$$\left(-x\right)a=16-3x-x^{2}$$

Divide both sides by -x.

$$\frac{\left(-x\right)a}{-x}=\frac{16-3x-x^{2}}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$a=\frac{16-3x-x^{2}}{-x}$$

Divide 16-3x-x^{2} by -x.

$$a=x+3-\frac{16}{x}$$

Solve for x

$$x=\frac{\sqrt{a^{2}-6a+73}+a-3}{2}$$

$$x=\frac{-\sqrt{a^{2}-6a+73}+a-3}{2}$$