(6+9a)*(2a+5)=

Solution for (6+9a)*(2a+5)= equation:

Simplifying
(6 + 9a)(2a + 5) = 0

Reorder the terms:
(6 + 9a)(5 + 2a) = 0

Multiply (6 + 9a) * (5 + 2a)
(6(5 + 2a) + 9a * (5 + 2a)) = 0
((5 * 6 + 2a * 6) + 9a * (5 + 2a)) = 0
((30 + 12a) + 9a * (5 + 2a)) = 0
(30 + 12a + (5 * 9a + 2a * 9a)) = 0
(30 + 12a + (45a + 18a2)) = 0

Combine like terms: 12a + 45a = 57a
(30 + 57a + 18a2) = 0

Solving
30 + 57a + 18a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 19a + 6a2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + 2a)' equal to zero and attempt to solve:

Simplifying
5 + 2a = 0

Solving
5 + 2a = 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 + 2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2a = 0 + -5
2a = 0 + -5

Combine like terms: 0 + -5 = -5
2a = -5

Divide each side by '2'.
a = -2.5

Simplifying
a = -2.5
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 = {-2.5, -0.6666666667}