(3a-5)(2a+6)=

Solution for (3a-5)(2a+6)= equation:

Simplifying
(3a + -5)(2a + 6) = 0

Reorder the terms:
(-5 + 3a)(2a + 6) = 0

Reorder the terms:
(-5 + 3a)(6 + 2a) = 0

Multiply (-5 + 3a) * (6 + 2a)
(-5(6 + 2a) + 3a * (6 + 2a)) = 0
((6 * -5 + 2a * -5) + 3a * (6 + 2a)) = 0
((-30 + -10a) + 3a * (6 + 2a)) = 0
(-30 + -10a + (6 * 3a + 2a * 3a)) = 0
(-30 + -10a + (18a + 6a2)) = 0

Combine like terms: -10a + 18a = 8a
(-30 + 8a + 6a2) = 0

Solving
-30 + 8a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 4a + 3a2) = 0

Factor a trinomial.
2((-3 + -1a)(5 + -3a)) = 0

Ignore the factor 2.
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 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 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 + -3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3a = 0 + -5
-3a = 0 + -5

Combine like terms: 0 + -5 = -5
-3a = -5

Divide each side by '-3'.
a = 1.666666667

Simplifying
a = 1.666666667
Solution
a = {-3, 1.666666667}