r2+7r+12=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 12 and whose sum is 7.

3,4

Write the factored form using these integers.

(r+3)(r+4)=0

(r+3)(r+4)=0

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

r+3=0

r+4=0

Set the first factor equal to 0.

r+3=0

Subtract 3 from both sides of the equation.

r=-3

r=-3

Set the next factor equal to 0.

r+4=0

Subtract 4 from both sides of the equation.

r=-4

r=-4

The final solution is all the values that make (r+3)(r+4)=0 true.

r=-3,-4

Solve for r r^2+7r+12=0