7a^2+34a+40=0

Solution for 7a^2+34a+40=0 equation:

Simplifying
7a2 + 34a + 40 = 0

Reorder the terms:
40 + 34a + 7a2 = 0

Solving
40 + 34a + 7a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(20 + 7a)(2 + a) = 0

Subproblem 1
Set the factor '(20 + 7a)' equal to zero and attempt to solve:

Simplifying
20 + 7a = 0

Solving
20 + 7a = 0

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

Add '-20' to each side of the equation.
20 + -20 + 7a = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 7a = 0 + -20
7a = 0 + -20

Combine like terms: 0 + -20 = -20
7a = -20

Divide each side by '7'.
a = -2.857142857

Simplifying
a = -2.857142857
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 = {-2.857142857, -2}