n2+6n=40

Move 40 to the left side of the equation by subtracting it from both sides.

n2+6n-40=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 -40 and whose sum is 6.

-4,10

Write the factored form using these integers.

(n-4)(n+10)=0

(n-4)(n+10)=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-4=0

n+10=0

Set the first factor equal to 0.

n-4=0

Add 4 to both sides of the equation.

n=4

n=4

Set the next factor equal to 0.

n+10=0

Subtract 10 from both sides of the equation.

n=-10

n=-10

The final solution is all the values that make (n-4)(n+10)=0 true.

n=4,-10

Solve using the Square Root Property n^2+6n=40