n(4n+14)=-10

Solution for n(4n+14)=-10 equation:

Simplifying
n(4n + 14) = -10

Reorder the terms:
n(14 + 4n) = -10
(14 * n + 4n * n) = -10
(14n + 4n2) = -10

Solving
14n + 4n2 = -10

Solving for variable 'n'.

Reorder the terms:
10 + 14n + 4n2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + 14n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 7n + 2n2) = 0

Factor a trinomial.
2((5 + 2n)(1 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 2n)' equal to zero and attempt to solve:

Simplifying
5 + 2n = 0

Solving
5 + 2n = 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 + 2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2n = 0 + -5
2n = 0 + -5

Combine like terms: 0 + -5 = -5
2n = -5

Divide each side by '2'.
n = -2.5

Simplifying
n = -2.5
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 = {-2.5, -1}