z2+10z+24=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 24 and whose sum is 10.

4,6

Write the factored form using these integers.

(z+4)(z+6)=0

(z+4)(z+6)=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+4=0

z+6=0

Set the first factor equal to 0.

z+4=0

Subtract 4 from both sides of the equation.

z=-4

z=-4

Set the next factor equal to 0.

z+6=0

Subtract 6 from both sides of the equation.

z=-6

z=-6

The final solution is all the values that make (z+4)(z+6)=0 true.

z=-4,-6

Solve for z z^2+10z+24=0