10a^2-16a+6=0

Solution for 10a^2-16a+6=0 equation:

Simplifying
10a2 + -16a + 6 = 0

Reorder the terms:
6 + -16a + 10a2 = 0

Solving
6 + -16a + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -8a + 5a2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
a = {0.6, 1}