A2+A=72

Move 72 to the left side of the equation by subtracting it from both sides.

A2+A-72=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 -72 and whose sum is 1.

-8,9

Write the factored form using these integers.

(A-8)(A+9)=0

(A-8)(A+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.

A-8=0

A+9=0

Set the first factor equal to 0.

A-8=0

Add 8 to both sides of the equation.

A=8

A=8

Set the next factor equal to 0.

A+9=0

Subtract 9 from both sides of the equation.

A=-9

A=-9

The final solution is all the values that make (A-8)(A+9)=0 true.

A=8,-9

Solve for A A^2+A=72