(11a+3)(3a-9)=0

Solution for (11a+3)(3a-9)=0 equation:

Simplifying
(11a + 3)(3a + -9) = 0

Reorder the terms:
(3 + 11a)(3a + -9) = 0

Reorder the terms:
(3 + 11a)(-9 + 3a) = 0

Multiply (3 + 11a) * (-9 + 3a)
(3(-9 + 3a) + 11a * (-9 + 3a)) = 0
((-9 * 3 + 3a * 3) + 11a * (-9 + 3a)) = 0
((-27 + 9a) + 11a * (-9 + 3a)) = 0
(-27 + 9a + (-9 * 11a + 3a * 11a)) = 0
(-27 + 9a + (-99a + 33a2)) = 0

Combine like terms: 9a + -99a = -90a
(-27 + -90a + 33a2) = 0

Solving
-27 + -90a + 33a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -30a + 11a2) = 0

Factor a trinomial.
3((-3 + -11a)(3 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -11a)' equal to zero and attempt to solve:

Simplifying
-3 + -11a = 0

Solving
-3 + -11a = 0

Move all terms containing a to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -11a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -11a = 0 + 3
-11a = 0 + 3

Combine like terms: 0 + 3 = 3
-11a = 3

Divide each side by '-11'.
a = -0.2727272727

Simplifying
a = -0.2727272727
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.2727272727, 3}