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

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

Solve for x

$$x=\frac{3}{4}=0.75$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

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

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

Consider \left(x-2\right)\left(x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$-2x-2=x^{2}-4-\left(x-1\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$-2x-2=x^{2}-4-\left(x^{2}-2x+1\right)$$

To find the opposite of x^{2}-2x+1, find the opposite of each term.

$$-2x-2=x^{2}-4-x^{2}+2x-1$$

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

$$-2x-2=-4+2x-1$$

Subtract 1 from -4 to get -5.

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

Subtract 2x from both sides.

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

Combine -2x and -2x to get -4x.

$$-4x-2=-5$$

Add 2 to both sides.

$$-4x=-5+2$$

Add -5 and 2 to get -3.

$$-4x=-3$$

Divide both sides by -4.

$$x=\frac{-3}{-4}$$

Fraction \frac{-3}{-4} can be simplified to \frac{3}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{3}{4}$$