10(n^2+n)-6(n^2-2)=

Solution for 10(n^2+n)-6(n^2-2)= equation:

Simplifying
10(n2 + n) + -6(n2 + -2) = 0

Reorder the terms:
10(n + n2) + -6(n2 + -2) = 0
(n * 10 + n2 * 10) + -6(n2 + -2) = 0
(10n + 10n2) + -6(n2 + -2) = 0

Reorder the terms:
10n + 10n2 + -6(-2 + n2) = 0
10n + 10n2 + (-2 * -6 + n2 * -6) = 0
10n + 10n2 + (12 + -6n2) = 0

Reorder the terms:
12 + 10n + 10n2 + -6n2 = 0

Combine like terms: 10n2 + -6n2 = 4n2
12 + 10n + 4n2 = 0

Solving
12 + 10n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 5n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 5n + 2n2)' equal to zero and attempt to solve:

Simplifying
6 + 5n + 2n2 = 0

Solving
6 + 5n + 2n2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
3 + 2.5n + n2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2.5n + -3 + n2 = 0 + -3

Reorder the terms:
3 + -3 + 2.5n + n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2.5n + n2 = 0 + -3
2.5n + n2 = 0 + -3

Combine like terms: 0 + -3 = -3
2.5n + n2 = -3

The n term is 2.5n.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5n + 1.5625 + n2 = -3 + 1.5625

Reorder the terms:
1.5625 + 2.5n + n2 = -3 + 1.5625

Combine like terms: -3 + 1.5625 = -1.4375
1.5625 + 2.5n + n2 = -1.4375

Factor a perfect square on the left side:
(n + 1.25)(n + 1.25) = -1.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.