10a^2+-65a+30=0

Solution for 10a^2+-65a+30=0 equation:

Simplifying
10a2 + -65a + 30 = 0

Reorder the terms:
30 + -65a + 10a2 = 0

Solving
30 + -65a + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -13a + 2a2) = 0

Factor a trinomial.
5((1 + -2a)(6 + -1a)) = 0

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

Simplifying
1 + -2a = 0

Solving
1 + -2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a = 0 + -1
-2a = 0 + -1

Combine like terms: 0 + -1 = -1
-2a = -1

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 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 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {0.5, 6}