10n^2+98n+72=0

Solution for 10n^2+98n+72=0 equation:

Simplifying
10n2 + 98n + 72 = 0

Reorder the terms:
72 + 98n + 10n2 = 0

Solving
72 + 98n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + 49n + 5n2) = 0

Factor a trinomial.
2((9 + n)(4 + 5n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + n)' equal to zero and attempt to solve:

Simplifying
9 + n = 0

Solving
9 + n = 0

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

Add '-9' to each side of the equation.
9 + -9 + n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + n = 0 + -9
n = 0 + -9

Combine like terms: 0 + -9 = -9
n = -9

Simplifying
n = -9
Subproblem 2
Set the factor '(4 + 5n)' equal to zero and attempt to solve:

Simplifying
4 + 5n = 0

Solving
4 + 5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5n = 0 + -4
5n = 0 + -4

Combine like terms: 0 + -4 = -4
5n = -4

Divide each side by '5'.
n = -0.8

Simplifying
n = -0.8
Solution
n = {-9, -0.8}