10a^2-13a-3=0

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

Simplifying
10a2 + -13a + -3 = 0

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

Solving
-3 + -13a + 10a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -5a)(3 + -2a) = 0

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

Simplifying
-1 + -5a = 0

Solving
-1 + -5a = 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 + -5a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5a = 0 + 1
-5a = 0 + 1

Combine like terms: 0 + 1 = 1
-5a = 1

Divide each side by '-5'.
a = -0.2

Simplifying
a = -0.2
Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-0.2, 1.5}