(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((-3 + -1a)(5 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
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
Solution
a = {-3, 5}