a2=-35-12a

Add 12a to both sides of the equation.

a2+12a=-35

Move 35 to the left side of the equation by adding it to both sides.

a2+12a+35=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 35 and whose sum is 12.

5,7

Write the factored form using these integers.

(a+5)(a+7)=0

(a+5)(a+7)=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+5=0

a+7=0

Set the first factor equal to 0.

a+5=0

Subtract 5 from both sides of the equation.

a=-5

a=-5

Set the next factor equal to 0.

a+7=0

Subtract 7 from both sides of the equation.

a=-7

a=-7

The final solution is all the values that make (a+5)(a+7)=0 true.

a=-5,-7

Solve for a a^2=-35-12a