Solve (x-1)*(x+3)=(x+2)*(x-3)+1

$$( x - 1 ) \times ( x + 3 ) = ( x + 2 ) \times ( x - 3 ) + 1$$

Solve for x

$$x=-\frac{2}{3}\approx -0.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by x+3 and combine like terms.

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

Use the distributive property to multiply x+2 by x-3 and combine like terms.

$$x^{2}+2x-3=x^{2}-x-6+1$$

Add -6 and 1 to get -5.

$$x^{2}+2x-3=x^{2}-x-5$$

Subtract x^{2} from both sides.

$$x^{2}+2x-3-x^{2}=-x-5$$

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

$$2x-3=-x-5$$

Add x to both sides.

$$2x-3+x=-5$$

Combine 2x and x to get 3x.

$$3x-3=-5$$

Add 3 to both sides.

$$3x=-5+3$$

Add -5 and 3 to get -2.

$$3x=-2$$

Divide both sides by 3.

$$x=\frac{-2}{3}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$x=-\frac{2}{3}$$