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

n2+15n+53=-3
Move 3 to the left side of the equation by adding it to both sides.
n2+15n+53+3=0
n2+15n+56=0
Factor n2+15n+56 using the AC method.
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 and solve.
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 and solve.
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

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