42a^2+19a+2=0

Solution for 42a^2+19a+2=0 equation:

Simplifying
42a2 + 19a + 2 = 0

Reorder the terms:
2 + 19a + 42a2 = 0

Solving
2 + 19a + 42a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + 7a)(1 + 6a) = 0

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

Simplifying
2 + 7a = 0

Solving
2 + 7a = 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 + 7a = 0 + -2

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

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

Divide each side by '7'.
a = -0.2857142857

Simplifying
a = -0.2857142857
Subproblem 2
Set the factor '(1 + 6a)' equal to zero and attempt to solve:

Simplifying
1 + 6a = 0

Solving
1 + 6a = 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 + 6a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6a = 0 + -1
6a = 0 + -1

Combine like terms: 0 + -1 = -1
6a = -1

Divide each side by '6'.
a = -0.1666666667

Simplifying
a = -0.1666666667
Solution
a = {-0.2857142857, -0.1666666667}