(a+6)(3a+7)=0

Solution for (a+6)(3a+7)=0 equation:

Simplifying
(a + 6)(3a + 7) = 0

Reorder the terms:
(6 + a)(3a + 7) = 0

Reorder the terms:
(6 + a)(7 + 3a) = 0

Multiply (6 + a) * (7 + 3a)
(6(7 + 3a) + a(7 + 3a)) = 0
((7 * 6 + 3a * 6) + a(7 + 3a)) = 0
((42 + 18a) + a(7 + 3a)) = 0
(42 + 18a + (7 * a + 3a * a)) = 0
(42 + 18a + (7a + 3a2)) = 0

Combine like terms: 18a + 7a = 25a
(42 + 25a + 3a2) = 0

Solving
42 + 25a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6 + a)(7 + 3a) = 0

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

Simplifying
6 + a = 0

Solving
6 + a = 0

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

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(7 + 3a)' equal to zero and attempt to solve:

Simplifying
7 + 3a = 0

Solving
7 + 3a = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3a = 0 + -7
3a = 0 + -7

Combine like terms: 0 + -7 = -7
3a = -7

Divide each side by '3'.
a = -2.333333333

Simplifying
a = -2.333333333
Solution
a = {-6, -2.333333333}