7n^3+19n^2+10n=0

Solution for 7n^3+19n^2+10n=0 equation:

Simplifying
7n3 + 19n2 + 10n = 0

Reorder the terms:
10n + 19n2 + 7n3 = 0

Solving
10n + 19n2 + 7n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(10 + 19n + 7n2) = 0

Factor a trinomial.
n((2 + n)(5 + 7n)) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Subproblem 3
Set the factor '(5 + 7n)' equal to zero and attempt to solve:

Simplifying
5 + 7n = 0

Solving
5 + 7n = 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 + 7n = 0 + -5

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

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

Divide each side by '7'.
n = -0.7142857143

Simplifying
n = -0.7142857143
Solution
n = {0, -2, -0.7142857143}