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

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

Solve for x

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

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x-\frac{2}{3} by x.

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

Subtract x^{2} from both sides.

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

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

$$-2x+1=-\frac{2}{3}x$$

Add \frac{2}{3}x to both sides.

$$-2x+1+\frac{2}{3}x=0$$

Combine -2x and \frac{2}{3}x to get -\frac{4}{3}x.

$$-\frac{4}{3}x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{4}{3}x=-1$$

Multiply both sides by -\frac{3}{4}, the reciprocal of -\frac{4}{3}.

$$x=-\left(-\frac{3}{4}\right)$$

Multiply -1 and -\frac{3}{4} to get \frac{3}{4}.

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