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

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

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

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

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

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

Combine like terms: 5a + 18a = 23a
(30 + 23a + 3a2) = 0

Solving
30 + 23a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6 + a)(5 + 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 '(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 = {-6, -1.666666667}