21a^2-57a+30=0

Solution for 21a^2-57a+30=0 equation:

Simplifying
21a2 + -57a + 30 = 0

Reorder the terms:
30 + -57a + 21a2 = 0

Solving
30 + -57a + 21a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -19a + 7a2) = 0

Factor a trinomial.
3((5 + -7a)(2 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -7a)' equal to zero and attempt to solve:

Simplifying
5 + -7a = 0

Solving
5 + -7a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -7a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7a = 0 + -5
-7a = 0 + -5

Combine like terms: 0 + -5 = -5
-7a = -5

Divide each side by '-7'.
a = 0.7142857143

Simplifying
a = 0.7142857143
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {0.7142857143, 2}