25a^2+65a+30=0

Solution for 25a^2+65a+30=0 equation:

Simplifying
25a2 + 65a + 30 = 0

Reorder the terms:
30 + 65a + 25a2 = 0

Solving
30 + 65a + 25a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + 13a + 5a2) = 0

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

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

Simplifying
2 + a = 0

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

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

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

Simplifying
a = -2
Subproblem 2
Set the factor '(3 + 5a)' equal to zero and attempt to solve:

Simplifying
3 + 5a = 0

Solving
3 + 5a = 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 + 5a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5a = 0 + -3
5a = 0 + -3

Combine like terms: 0 + -3 = -3
5a = -3

Divide each side by '5'.
a = -0.6

Simplifying
a = -0.6
Solution
a = {-2, -0.6}