n2-10n+21=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 21 and whose sum is -10.

-7,-3

Write the factored form using these integers.

(n-7)(n-3)=0

(n-7)(n-3)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

n-7=0

n-3=0

Set the first factor equal to 0.

n-7=0

Add 7 to both sides of the equation.

n=7

n=7

Set the next factor equal to 0.

n-3=0

Add 3 to both sides of the equation.

n=3

n=3

The final solution is all the values that make (n-7)(n-3)=0 true.

n=7,3

Solve for n n^2-10n+21=0