5n^2+12n+7=0

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

Simplifying
5n2 + 12n + 7 = 0

Reorder the terms:
7 + 12n + 5n2 = 0

Solving
7 + 12n + 5n2 = 0

Solving for variable 'n'.

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

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

Simplifying
7 + 5n = 0

Solving
7 + 5n = 0

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

Add '-7' to each side of the equation.
7 + -7 + 5n = 0 + -7

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

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

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

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

Add '-1' to each side of the equation.
1 + -1 + n = 0 + -1

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

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

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