z2+14z+45=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 45 and whose sum is 14.

5,9

Write the factored form using these integers.

(z+5)(z+9)=0

(z+5)(z+9)=0

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

z+5=0

z+9=0

Set the first factor equal to 0.

z+5=0

Subtract 5 from both sides of the equation.

z=-5

z=-5

Set the next factor equal to 0.

z+9=0

Subtract 9 from both sides of the equation.

z=-9

z=-9

The final solution is all the values that make (z+5)(z+9)=0 true.

z=-5,-9

Solve for z z^2+14z+45=0