-2n(n+1)-3=1

Solution for -2n(n+1)-3=1 equation:

Simplifying
-2n(n + 1) + -3 = 1

Reorder the terms:
-2n(1 + n) + -3 = 1
(1 * -2n + n * -2n) + -3 = 1
(-2n + -2n2) + -3 = 1

Reorder the terms:
-3 + -2n + -2n2 = 1

Solving
-3 + -2n + -2n2 = 1

Solving for variable 'n'.

Reorder the terms:
-3 + -1 + -2n + -2n2 = 1 + -1

Combine like terms: -3 + -1 = -4
-4 + -2n + -2n2 = 1 + -1

Combine like terms: 1 + -1 = 0
-4 + -2n + -2n2 = 0

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

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

Simplifying
2 + n + n2 = 0

Solving
2 + n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + n + n2 = 0 + -2

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

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

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
n + 0.25 + n2 = -2 + 0.25

Reorder the terms:
0.25 + n + n2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + n + n2 = -1.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -1.75

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.