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

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

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by x+2 and combine like terms.

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

Use the distributive property to multiply x by x+3.

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

To find the opposite of x^{2}+3x, find the opposite of each term.

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

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

$$x-2-3x=x-1$$

Combine x and -3x to get -2x.

$$-2x-2=x-1$$

Subtract x from both sides.

$$-2x-2-x=-1$$

Combine -2x and -x to get -3x.

$$-3x-2=-1$$

Add 2 to both sides.

$$-3x=-1+2$$

Add -1 and 2 to get 1.

$$-3x=1$$

Divide both sides by -3.

$$x=\frac{1}{-3}$$

Fraction \frac{1}{-3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$x=-\frac{1}{3}$$