-10n^2=2n+3

Solution for -10n^2=2n+3 equation:

Simplifying
-10n2 = 2n + 3

Reorder the terms:
-10n2 = 3 + 2n

Solving
-10n2 = 3 + 2n

Solving for variable 'n'.

Reorder the terms:
-3 + -2n + -10n2 = 3 + 2n + -3 + -2n

Reorder the terms:
-3 + -2n + -10n2 = 3 + -3 + 2n + -2n

Combine like terms: 3 + -3 = 0
-3 + -2n + -10n2 = 0 + 2n + -2n
-3 + -2n + -10n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-3 + -2n + -10n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 2n + 10n2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 2n + 10n2)' equal to zero and attempt to solve:

Simplifying
3 + 2n + 10n2 = 0

Solving
3 + 2n + 10n2 = 0

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

Divide each side by '10'.
0.3 + 0.2n + n2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + 0.2n + -0.3 + n2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + 0.2n + n2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + 0.2n + n2 = 0.0 + -0.3
0.2n + n2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
0.2n + n2 = -0.3

The n term is 0.2n.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2n + 0.01 + n2 = -0.3 + 0.01

Reorder the terms:
0.01 + 0.2n + n2 = -0.3 + 0.01

Combine like terms: -0.3 + 0.01 = -0.29
0.01 + 0.2n + n2 = -0.29

Factor a perfect square on the left side:
(n + 0.1)(n + 0.1) = -0.29

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.