7a^2+17a+6=0

Solution for 7a^2+17a+6=0 equation:

Simplifying
7a2 + 17a + 6 = 0

Reorder the terms:
6 + 17a + 7a2 = 0

Solving
6 + 17a + 7a2 = 0

Solving for variable 'a'.

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

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

Simplifying
2 + a = 0

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

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

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

Simplifying
a = -2
Subproblem 2
Set the factor '(3 + 7a)' equal to zero and attempt to solve:

Simplifying
3 + 7a = 0

Solving
3 + 7a = 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 + 7a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7a = 0 + -3
7a = 0 + -3

Combine like terms: 0 + -3 = -3
7a = -3

Divide each side by '7'.
a = -0.4285714286

Simplifying
a = -0.4285714286
Solution
a = {-2, -0.4285714286}