(11a+6)(5a-15)=0

Solution for (11a+6)(5a-15)=0 equation:

Simplifying
(11a + 6)(5a + -15) = 0

Reorder the terms:
(6 + 11a)(5a + -15) = 0

Reorder the terms:
(6 + 11a)(-15 + 5a) = 0

Multiply (6 + 11a) * (-15 + 5a)
(6(-15 + 5a) + 11a * (-15 + 5a)) = 0
((-15 * 6 + 5a * 6) + 11a * (-15 + 5a)) = 0
((-90 + 30a) + 11a * (-15 + 5a)) = 0
(-90 + 30a + (-15 * 11a + 5a * 11a)) = 0
(-90 + 30a + (-165a + 55a2)) = 0

Combine like terms: 30a + -165a = -135a
(-90 + -135a + 55a2) = 0

Solving
-90 + -135a + 55a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + -27a + 11a2) = 0

Factor a trinomial.
5((-6 + -11a)(3 + -1a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -11a)' equal to zero and attempt to solve:

Simplifying
-6 + -11a = 0

Solving
-6 + -11a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -11a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -11a = 0 + 6
-11a = 0 + 6

Combine like terms: 0 + 6 = 6
-11a = 6

Divide each side by '-11'.
a = -0.5454545455

Simplifying
a = -0.5454545455
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 = {-0.5454545455, 3}