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

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

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

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

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

Multiply (4 + 6a) * (6 + 4a)
(4(6 + 4a) + 6a * (6 + 4a)) = 0
((6 * 4 + 4a * 4) + 6a * (6 + 4a)) = 0
((24 + 16a) + 6a * (6 + 4a)) = 0
(24 + 16a + (6 * 6a + 4a * 6a)) = 0
(24 + 16a + (36a + 24a2)) = 0

Combine like terms: 16a + 36a = 52a
(24 + 52a + 24a2) = 0

Solving
24 + 52a + 24a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 13a + 6a2) = 0

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

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

Simplifying
3 + 2a = 0

Solving
3 + 2a = 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 + 2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2a = 0 + -3
2a = 0 + -3

Combine like terms: 0 + -3 = -3
2a = -3

Divide each side by '2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 2
Set the factor '(2 + 3a)' equal to zero and attempt to solve:

Simplifying
2 + 3a = 0

Solving
2 + 3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3a = 0 + -2
3a = 0 + -2

Combine like terms: 0 + -2 = -2
3a = -2

Divide each side by '3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
Solution
a = {-1.5, -0.6666666667}