Solve (x-3)(x-2)-3(x-1)=left(x-1right)^2-1

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

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

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

$$x^{2}-5x+6-3\left(x-1\right)=\left(x-1\right)^{2}-1$$

Use the distributive property to multiply -3 by x-1.

$$x^{2}-5x+6-3x+3=\left(x-1\right)^{2}-1$$

Combine -5x and -3x to get -8x.

$$x^{2}-8x+6+3=\left(x-1\right)^{2}-1$$

Add 6 and 3 to get 9.

$$x^{2}-8x+9=\left(x-1\right)^{2}-1$$

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

$$x^{2}-8x+9=x^{2}-2x+1-1$$

Subtract 1 from 1 to get 0.

$$x^{2}-8x+9=x^{2}-2x$$

Subtract x^{2} from both sides.

$$x^{2}-8x+9-x^{2}=-2x$$

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

$$-8x+9=-2x$$

Add 2x to both sides.

$$-8x+9+2x=0$$

Combine -8x and 2x to get -6x.

$$-6x+9=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-6x=-9$$

Divide both sides by -6.

$$x=\frac{-9}{-6}$$

Reduce the fraction \frac{-9}{-6} to lowest terms by extracting and canceling out -3.

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