3a^2+13a+14=0

Solution for 3a^2+13a+14=0 equation:

Simplifying
3a2 + 13a + 14 = 0

Reorder the terms:
14 + 13a + 3a2 = 0

Solving
14 + 13a + 3a2 = 0

Solving for variable 'a'.

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

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

Simplifying
7 + 3a = 0

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

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

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

Divide each side by '3'.
a = -2.333333333

Simplifying
a = -2.333333333
Subproblem 2
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
Solution
a = {-2.333333333, -2}