-10a^2+21a-9=0

Solution for -10a^2+21a-9=0 equation:

Simplifying
-10a2 + 21a + -9 = 0

Reorder the terms:
-9 + 21a + -10a2 = 0

Solving
-9 + 21a + -10a2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {1.5, 0.6}