a3-9a-11a2=-99

Move 99 to the left side of the equation by adding it to both sides.

a3-9a-11a2+99=0

Reorder terms.

a3-11a2-9a+99=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(a3-11a2)-9a+99=0

Factor out the greatest common factor (GCF) from each group.

a2(a-11)-9(a-11)=0

a2(a-11)-9(a-11)=0

Factor the polynomial by factoring out the greatest common factor, a-11.

(a-11)(a2-9)=0

Rewrite 9 as 32.

(a-11)(a2-32)=0

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=3.

(a-11)((a+3)(a-3))=0

Remove unnecessary parentheses.

(a-11)(a+3)(a-3)=0

(a-11)(a+3)(a-3)=0

(a-11)(a+3)(a-3)=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-11=0

a+3=0

a-3=0

Set the first factor equal to 0.

a-11=0

Add 11 to both sides of the equation.

a=11

a=11

Set the next factor equal to 0.

a+3=0

Subtract 3 from both sides of the equation.

a=-3

a=-3

Set the next factor equal to 0.

a-3=0

Add 3 to both sides of the equation.

a=3

a=3

The final solution is all the values that make (a-11)(a+3)(a-3)=0 true.

a=11,-3,3

Solve for a a^3-9a-11a^2=-99