6x=cos(x)

Solution for 6x=cos(x) equation:

Simplifying
6x = cos(x)

Multiply cos * x
6x = cosx

Solving
6x = cosx

Solving for variable 'x'.

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

Add '-1cosx' to each side of the equation.
-1cosx + 6x = cosx + -1cosx

Combine like terms: cosx + -1cosx = 0
-1cosx + 6x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1cos + 6) = 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 '(-1cos + 6)' equal to zero and attempt to solve:

Simplifying
-1cos + 6 = 0

Reorder the terms:
6 + -1cos = 0

Solving
6 + -1cos = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1cos = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1cos = 0 + -6
-1cos = 0 + -6

Combine like terms: 0 + -6 = -6
-1cos = -6

Add 'cos' to each side of the equation.
-1cos + cos = -6 + cos

Combine like terms: -1cos + cos = 0
0 = -6 + cos

Simplifying
0 = -6 + cos

The solution to this equation could not be determined.

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