Solve (x-2)^2+5(2-x)=(x+1)(x-1)

$$( x - 2 ) ^ { 2 } + 5 ( 2 - x ) = ( x + 1 ) ( x - 1 )$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

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

$$x^{2}-4x+4+5\left(2-x\right)=\left(x+1\right)\left(x-1\right)$$

Use the distributive property to multiply 5 by 2-x.

$$x^{2}-4x+4+10-5x=\left(x+1\right)\left(x-1\right)$$

Add 4 and 10 to get 14.

$$x^{2}-4x+14-5x=\left(x+1\right)\left(x-1\right)$$

Combine -4x and -5x to get -9x.

$$x^{2}-9x+14=\left(x+1\right)\left(x-1\right)$$

Consider \left(x+1\right)\left(x-1\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 1.

$$x^{2}-9x+14=x^{2}-1$$

Subtract x^{2} from both sides.

$$x^{2}-9x+14-x^{2}=-1$$

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

$$-9x+14=-1$$

Subtract 14 from both sides.

$$-9x=-1-14$$

Subtract 14 from -1 to get -15.

$$-9x=-15$$

Divide both sides by -9.

$$x=\frac{-15}{-9}$$

Reduce the fraction \frac{-15}{-9} to lowest terms by extracting and canceling out -3.

$$x=\frac{5}{3}$$