# Solve for a a^3-9a-11a^2=-99 a3-9a-11a2=-99
Move 99 to the left side of the equation by adding it to both sides.
a3-9a-11a2+99=0
Factor the left side of the equation.
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 and solve.
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 and solve.
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 and solve.
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

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