(2a-6)(3a+15)=0

Solution for (2a-6)(3a+15)=0 equation:

Simplifying
(2a + -6)(3a + 15) = 0

Reorder the terms:
(-6 + 2a)(3a + 15) = 0

Reorder the terms:
(-6 + 2a)(15 + 3a) = 0

Multiply (-6 + 2a) * (15 + 3a)
(-6(15 + 3a) + 2a * (15 + 3a)) = 0
((15 * -6 + 3a * -6) + 2a * (15 + 3a)) = 0
((-90 + -18a) + 2a * (15 + 3a)) = 0
(-90 + -18a + (15 * 2a + 3a * 2a)) = 0
(-90 + -18a + (30a + 6a2)) = 0

Combine like terms: -18a + 30a = 12a
(-90 + 12a + 6a2) = 0

Solving
-90 + 12a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + 2a + a2) = 0

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

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

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
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 = {-5, 3}