V(x)=cos(2x)-sin(2x)

Solution for V(x)=cos(2x)-sin(2x) equation:

Simplifying
V(x) = cos(2x) + -1sin(2x)

Multiply V * x
xV = cos(2x) + -1sin(2x)

Remove parenthesis around (2x)
xV = cos * 2x + -1sin(2x)

Reorder the terms for easier multiplication:
xV = 2cos * x + -1sin(2x)

Multiply cos * x
xV = 2cosx + -1sin(2x)

Remove parenthesis around (2x)
xV = 2cosx + -1ins * 2x

Reorder the terms for easier multiplication:
xV = 2cosx + -1 * 2ins * x

Multiply -1 * 2
xV = 2cosx + -2ins * x

Multiply ins * x
xV = 2cosx + -2insx

Solving
xV = 2cosx + -2insx

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2cosx' to each side of the equation.
-2cosx + xV = 2cosx + -2cosx + -2insx

Combine like terms: 2cosx + -2cosx = 0
-2cosx + xV = 0 + -2insx
-2cosx + xV = -2insx

Add '2insx' to each side of the equation.
-2cosx + 2insx + xV = -2insx + 2insx

Combine like terms: -2insx + 2insx = 0
-2cosx + 2insx + xV = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2cos + 2ins + V) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-2cos + 2ins + V)' equal to zero and attempt to solve:

Simplifying
-2cos + 2ins + V = 0

Reorder the terms:
V + -2cos + 2ins = 0

Solving
V + -2cos + 2ins = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1V' to each side of the equation.
V + -2cos + -1V + 2ins = 0 + -1V

Reorder the terms:
V + -1V + -2cos + 2ins = 0 + -1V

Combine like terms: V + -1V = 0
0 + -2cos + 2ins = 0 + -1V
-2cos + 2ins = 0 + -1V
Remove the zero:
-2cos + 2ins = -1V

Add '2cos' to each side of the equation.
-2cos + 2cos + 2ins = -1V + 2cos

Combine like terms: -2cos + 2cos = 0
0 + 2ins = -1V + 2cos
2ins = -1V + 2cos

Add '-2ins' to each side of the equation.
2ins + -2ins = -1V + 2cos + -2ins

Combine like terms: 2ins + -2ins = 0
0 = -1V + 2cos + -2ins

Simplifying
0 = -1V + 2cos + -2ins

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}