(3a+4)(6a+2)=0

Solution for (3a+4)(6a+2)=0 equation:

Simplifying
(3a + 4)(6a + 2) = 0

Reorder the terms:
(4 + 3a)(6a + 2) = 0

Reorder the terms:
(4 + 3a)(2 + 6a) = 0

Multiply (4 + 3a) * (2 + 6a)
(4(2 + 6a) + 3a * (2 + 6a)) = 0
((2 * 4 + 6a * 4) + 3a * (2 + 6a)) = 0
((8 + 24a) + 3a * (2 + 6a)) = 0
(8 + 24a + (2 * 3a + 6a * 3a)) = 0
(8 + 24a + (6a + 18a2)) = 0

Combine like terms: 24a + 6a = 30a
(8 + 30a + 18a2) = 0

Solving
8 + 30a + 18a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 15a + 9a2) = 0

Factor a trinomial.
2((4 + 3a)(1 + 3a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 3a)' equal to zero and attempt to solve:

Simplifying
4 + 3a = 0

Solving
4 + 3a = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3a = 0 + -4
3a = 0 + -4

Combine like terms: 0 + -4 = -4
3a = -4

Divide each side by '3'.
a = -1.333333333

Simplifying
a = -1.333333333
Subproblem 2
Set the factor '(1 + 3a)' equal to zero and attempt to solve:

Simplifying
1 + 3a = 0

Solving
1 + 3a = 0

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

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

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

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

Divide each side by '3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
Solution
a = {-1.333333333, -0.3333333333}