105a^2+238a+105=0

Solution for 105a^2+238a+105=0 equation:

Simplifying
105a2 + 238a + 105 = 0

Reorder the terms:
105 + 238a + 105a2 = 0

Solving
105 + 238a + 105a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7'.
7(15 + 34a + 15a2) = 0

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

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

Simplifying
5 + 3a = 0

Solving
5 + 3a = 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 + 3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3a = 0 + -5
3a = 0 + -5

Combine like terms: 0 + -5 = -5
3a = -5

Divide each side by '3'.
a = -1.666666667

Simplifying
a = -1.666666667
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 = {-1.666666667, -0.6}