Solve (x-3)(x+6)=(x-4)(x-5)

$$(x-3)(x+6)=(x-4)(x-5)$$

Solve for x

$$x = \frac{19}{6} = 3\frac{1}{6} \approx 3.166666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-3 by x+6 and combine like terms.

$$x^{2}+3x-18=\left(x-4\right)\left(x-5\right)$$

Use the distributive property to multiply x-4 by x-5 and combine like terms.

$$x^{2}+3x-18=x^{2}-9x+20$$

Subtract x^{2} from both sides.

$$x^{2}+3x-18-x^{2}=-9x+20$$

Combine x^{2} and -x^{2} to get 0.

$$3x-18=-9x+20$$

Add 9x to both sides.

$$3x-18+9x=20$$

Combine 3x and 9x to get 12x.

$$12x-18=20$$

Add 18 to both sides.

$$12x=20+18$$

Add 20 and 18 to get 38.

$$12x=38$$

Divide both sides by 12.

$$x=\frac{38}{12}$$

Reduce the fraction \frac{38}{12} to lowest terms by extracting and canceling out 2.

$$x=\frac{19}{6}$$