n2+15n+53=-3

Move 3 to the left side of the equation by adding it to both sides.

n2+15n+53+3=0

Add 53 and 3.

n2+15n+56=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 56 and whose sum is 15.

7,8

Write the factored form using these integers.

(n+7)(n+8)=0

(n+7)(n+8)=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+8=0

Set the first factor equal to 0.

n+7=0

Subtract 7 from both sides of the equation.

n=-7

n=-7

Set the next factor equal to 0.

n+8=0

Subtract 8 from both sides of the equation.

n=-8

n=-8

The final solution is all the values that make (n+7)(n+8)=0 true.

n=-7,-8

Solve for n n^2+15n+53=-3