35n^2+180n+25=0

Solution for 35n^2+180n+25=0 equation:

Simplifying
35n2 + 180n + 25 = 0

Reorder the terms:
25 + 180n + 35n2 = 0

Solving
25 + 180n + 35n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + 36n + 7n2) = 0

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

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

Simplifying
5 + n = 0

Solving
5 + n = 0

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

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

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

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

Simplifying
n = -5
Subproblem 2
Set the factor '(1 + 7n)' equal to zero and attempt to solve:

Simplifying
1 + 7n = 0

Solving
1 + 7n = 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 + 7n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7n = 0 + -1
7n = 0 + -1

Combine like terms: 0 + -1 = -1
7n = -1

Divide each side by '7'.
n = -0.1428571429

Simplifying
n = -0.1428571429
Solution
n = {-5, -0.1428571429}