Solve y=7(n-4)(n-5)-n(n-1)

$$y = 7 ( n - 4 ) ( n - 5 ) - n ( n - 1 )$$

Solve for y

$$y=2\left(n-7\right)\left(3n-10\right)$$

Solution Steps

Use the distributive property to multiply 7 by n-4.

$$y=\left(7n-28\right)\left(n-5\right)-n\left(n-1\right)$$

Use the distributive property to multiply 7n-28 by n-5 and combine like terms.

$$y=7n^{2}-63n+140-n\left(n-1\right)$$

Use the distributive property to multiply n by n-1.

$$y=7n^{2}-63n+140-\left(n^{2}-n\right)$$

To find the opposite of n^{2}-n, find the opposite of each term.

$$y=7n^{2}-63n+140-n^{2}+n$$

Combine 7n^{2} and -n^{2} to get 6n^{2}.

$$y=6n^{2}-63n+140+n$$

Combine -63n and n to get -62n.

$$y=6n^{2}-62n+140$$

Solve for n (complex solution)

$$n=\frac{-\sqrt{6y+121}+31}{6}$$

$$n=\frac{\sqrt{6y+121}+31}{6}$$

Solve for n

$$n=\frac{-\sqrt{6y+121}+31}{6}$$

$$n=\frac{\sqrt{6y+121}+31}{6}\text{, }y\geq -\frac{121}{6}$$