10a^2+41a+21=0

Solution for 10a^2+41a+21=0 equation:

Simplifying
10a2 + 41a + 21 = 0

Reorder the terms:
21 + 41a + 10a2 = 0

Solving
21 + 41a + 10a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(7 + 2a)' equal to zero and attempt to solve:

Simplifying
7 + 2a = 0

Solving
7 + 2a = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2a = 0 + -7
2a = 0 + -7

Combine like terms: 0 + -7 = -7
2a = -7

Divide each side by '2'.
a = -3.5

Simplifying
a = -3.5
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 = {-3.5, -0.6}