cos^2x-(3a+2)cosx+a+6=0

Solution for cos^2x-(3a+2)cosx+a+6=0 equation:

Simplifying
cos2x + -1(3a + 2) * cosx + a + 6 = 0

Reorder the terms:
cos2x + -1(2 + 3a) * cosx + a + 6 = 0

Reorder the terms for easier multiplication:
cos2x + -1cosx(2 + 3a) + a + 6 = 0
cos2x + (2 * -1cosx + 3a * -1cosx) + a + 6 = 0

Reorder the terms:
cos2x + (-3acosx + -2cosx) + a + 6 = 0
cos2x + (-3acosx + -2cosx) + a + 6 = 0

Reorder the terms:
6 + a + -3acosx + -2cosx + cos2x = 0

Solving
6 + a + -3acosx + -2cosx + cos2x = 0

Solving for variable 'a'.

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

Add '-6' to each side of the equation.
6 + a + -3acosx + -2cosx + -6 + cos2x = 0 + -6

Reorder the terms:
6 + -6 + a + -3acosx + -2cosx + cos2x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a + -3acosx + -2cosx + cos2x = 0 + -6
a + -3acosx + -2cosx + cos2x = 0 + -6

Combine like terms: 0 + -6 = -6
a + -3acosx + -2cosx + cos2x = -6

Add '2cosx' to each side of the equation.
a + -3acosx + -2cosx + 2cosx + cos2x = -6 + 2cosx

Combine like terms: -2cosx + 2cosx = 0
a + -3acosx + 0 + cos2x = -6 + 2cosx
a + -3acosx + cos2x = -6 + 2cosx

Add '-1cos2x' to each side of the equation.
a + -3acosx + cos2x + -1cos2x = -6 + 2cosx + -1cos2x

Combine like terms: cos2x + -1cos2x = 0
a + -3acosx + 0 = -6 + 2cosx + -1cos2x
a + -3acosx = -6 + 2cosx + -1cos2x

Reorder the terms:
6 + a + -3acosx + -2cosx + cos2x = -6 + 2cosx + -1cos2x + 6 + -2cosx + cos2x

Reorder the terms:
6 + a + -3acosx + -2cosx + cos2x = -6 + 6 + 2cosx + -2cosx + -1cos2x + cos2x

Combine like terms: -6 + 6 = 0
6 + a + -3acosx + -2cosx + cos2x = 0 + 2cosx + -2cosx + -1cos2x + cos2x
6 + a + -3acosx + -2cosx + cos2x = 2cosx + -2cosx + -1cos2x + cos2x

Combine like terms: 2cosx + -2cosx = 0
6 + a + -3acosx + -2cosx + cos2x = 0 + -1cos2x + cos2x
6 + a + -3acosx + -2cosx + cos2x = -1cos2x + cos2x

Combine like terms: -1cos2x + cos2x = 0
6 + a + -3acosx + -2cosx + cos2x = 0

The solution to this equation could not be determined.