5a^2+12a+7=0

Solution for 5a^2+12a+7=0 equation:

Simplifying
5a2 + 12a + 7 = 0

Reorder the terms:
7 + 12a + 5a2 = 0

Solving
7 + 12a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7 + 5a)(1 + a) = 0

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

Simplifying
7 + 5a = 0

Solving
7 + 5a = 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 + 5a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5a = 0 + -7
5a = 0 + -7

Combine like terms: 0 + -7 = -7
5a = -7

Divide each side by '5'.
a = -1.4

Simplifying
a = -1.4
Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

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

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

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

Simplifying
a = -1
Solution
a = {-1.4, -1}