Solve y=1/3(1-sqrt{7}+1)(1-sqrt{7}-3)

$$y= \frac{ 1 }{ 3 } (1- \sqrt{ 7 } +1)(1- \sqrt{ 7 } -3)$$

Solve for y

$$y=1$$

Steps for Solving Linear Equation

Add 1 and 1 to get 2.

$$y=\frac{1}{3}\left(2-\sqrt{7}\right)\left(1-\sqrt{7}-3\right)$$

Subtract 3 from 1 to get -2.

$$y=\frac{1}{3}\left(2-\sqrt{7}\right)\left(-2-\sqrt{7}\right)$$

Use the distributive property to multiply \frac{1}{3} by 2-\sqrt{7}.

$$y=\left(\frac{1}{3}\times 2+\frac{1}{3}\left(-1\right)\sqrt{7}\right)\left(-2-\sqrt{7}\right)$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$y=\left(\frac{2}{3}+\frac{1}{3}\left(-1\right)\sqrt{7}\right)\left(-2-\sqrt{7}\right)$$

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

$$y=\left(\frac{2}{3}-\frac{1}{3}\sqrt{7}\right)\left(-2-\sqrt{7}\right)$$

Apply the distributive property by multiplying each term of \frac{2}{3}-\frac{1}{3}\sqrt{7} by each term of -2-\sqrt{7}.

$$y=\frac{2}{3}\left(-2\right)+\frac{2}{3}\left(-1\right)\sqrt{7}-\frac{1}{3}\sqrt{7}\left(-2\right)-\frac{1}{3}\sqrt{7}\left(-1\right)\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$y=\frac{2}{3}\left(-2\right)+\frac{2}{3}\left(-1\right)\sqrt{7}-\frac{1}{3}\sqrt{7}\left(-2\right)-\frac{1}{3}\times 7\left(-1\right)$$

Express \frac{2}{3}\left(-2\right) as a single fraction.

$$y=\frac{2\left(-2\right)}{3}+\frac{2}{3}\left(-1\right)\sqrt{7}-\frac{1}{3}\sqrt{7}\left(-2\right)-\frac{1}{3}\times 7\left(-1\right)$$

Multiply 2 and -2 to get -4.

$$y=\frac{-4}{3}+\frac{2}{3}\left(-1\right)\sqrt{7}-\frac{1}{3}\sqrt{7}\left(-2\right)-\frac{1}{3}\times 7\left(-1\right)$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$y=-\frac{4}{3}+\frac{2}{3}\left(-1\right)\sqrt{7}-\frac{1}{3}\sqrt{7}\left(-2\right)-\frac{1}{3}\times 7\left(-1\right)$$

Multiply \frac{2}{3} and -1 to get -\frac{2}{3}.

$$y=-\frac{4}{3}-\frac{2}{3}\sqrt{7}-\frac{1}{3}\sqrt{7}\left(-2\right)-\frac{1}{3}\times 7\left(-1\right)$$

Express -\frac{1}{3}\left(-2\right) as a single fraction.

$$y=-\frac{4}{3}-\frac{2}{3}\sqrt{7}+\frac{-\left(-2\right)}{3}\sqrt{7}-\frac{1}{3}\times 7\left(-1\right)$$

Multiply -1 and -2 to get 2.

$$y=-\frac{4}{3}-\frac{2}{3}\sqrt{7}+\frac{2}{3}\sqrt{7}-\frac{1}{3}\times 7\left(-1\right)$$

Combine -\frac{2}{3}\sqrt{7} and \frac{2}{3}\sqrt{7} to get 0.

$$y=-\frac{4}{3}-\frac{1}{3}\times 7\left(-1\right)$$

Express -\frac{1}{3}\times 7 as a single fraction.

$$y=-\frac{4}{3}+\frac{-7}{3}\left(-1\right)$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$y=-\frac{4}{3}-\frac{7}{3}\left(-1\right)$$

Multiply -\frac{7}{3} and -1 to get \frac{7}{3}.

$$y=-\frac{4}{3}+\frac{7}{3}$$

Since -\frac{4}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$y=\frac{-4+7}{3}$$

Add -4 and 7 to get 3.

$$y=\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$y=1$$

Assign y

$$y≔1$$