Solve (x-2/3)(x+2/3)=x^2-5x+1/3

$$( x - \frac { 2 } { 3 } ) ( x + \frac { 2 } { 3 } ) = x ^ { 2 } - \frac { 5 x + 1 } { 3 }$$

Solve for x

$$x=\frac{1}{15}\approx 0.066666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

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

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

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

Use the distributive property to multiply 3x-2 by x+\frac{2}{3} and combine like terms.

$$3x^{2}-\frac{4}{3}=3x^{2}-\left(5x+1\right)$$

To find the opposite of 5x+1, find the opposite of each term.

$$3x^{2}-\frac{4}{3}=3x^{2}-5x-1$$

Subtract 3x^{2} from both sides.

$$3x^{2}-\frac{4}{3}-3x^{2}=-5x-1$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-\frac{4}{3}=-5x-1$$

Swap sides so that all variable terms are on the left hand side.

$$-5x-1=-\frac{4}{3}$$

Add 1 to both sides.

$$-5x=-\frac{4}{3}+1$$

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

$$-5x=-\frac{1}{3}$$

Divide both sides by -5.

$$x=\frac{-\frac{1}{3}}{-5}$$

Express \frac{-\frac{1}{3}}{-5} as a single fraction.

$$x=\frac{-1}{3\left(-5\right)}$$

Multiply 3 and -5 to get -15.

$$x=\frac{-1}{-15}$$

Fraction \frac{-1}{-15} can be simplified to \frac{1}{15} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{15}$$