2n^2-4n=-42

Solution for 2n^2-4n=-42 equation:

Simplifying
2n2 + -4n = -42

Reorder the terms:
-4n + 2n2 = -42

Solving
-4n + 2n2 = -42

Solving for variable 'n'.

Reorder the terms:
42 + -4n + 2n2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + -4n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -2n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(21 + -2n + n2)' equal to zero and attempt to solve:

Simplifying
21 + -2n + n2 = 0

Solving
21 + -2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -2n + -21 + n2 = 0 + -21

Reorder the terms:
21 + -21 + -2n + n2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -2n + n2 = 0 + -21
-2n + n2 = 0 + -21

Combine like terms: 0 + -21 = -21
-2n + n2 = -21

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = -21 + 1

Reorder the terms:
1 + -2n + n2 = -21 + 1

Combine like terms: -21 + 1 = -20
1 + -2n + n2 = -20

Factor a perfect square on the left side:
(n + -1)(n + -1) = -20

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.