3a^2-13a+10=0

Solution for 3a^2-13a+10=0 equation:

Simplifying
3a2 + -13a + 10 = 0

Reorder the terms:
10 + -13a + 3a2 = 0

Solving
10 + -13a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -1a)(10 + -3a) = 0

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

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Subproblem 2
Set the factor '(10 + -3a)' equal to zero and attempt to solve:

Simplifying
10 + -3a = 0

Solving
10 + -3a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3a = 0 + -10
-3a = 0 + -10

Combine like terms: 0 + -10 = -10
-3a = -10

Divide each side by '-3'.
a = 3.333333333

Simplifying
a = 3.333333333
Solution
a = {1, 3.333333333}