x^2=x+3cos(2x)

Solution for x^2=x+3cos(2x) equation:

Simplifying
x2 = x + 3cos(2x)

Remove parenthesis around (2x)
x2 = x + 3cos * 2x

Reorder the terms for easier multiplication:
x2 = x + 3 * 2cos * x

Multiply 3 * 2
x2 = x + 6cos * x

Multiply cos * x
x2 = x + 6cosx

Reorder the terms:
x2 = 6cosx + x

Solving
x2 = 6cosx + x

Solving for variable 'x'.

Reorder the terms:
-6cosx + -1x + x2 = 6cosx + x + -6cosx + -1x

Reorder the terms:
-6cosx + -1x + x2 = 6cosx + -6cosx + x + -1x

Combine like terms: 6cosx + -6cosx = 0
-6cosx + -1x + x2 = 0 + x + -1x
-6cosx + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-6cosx + -1x + x2 = 0

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

Simplifying
-6cos + -1 + x = 0

Reorder the terms:
-1 + -6cos + x = 0

Solving
-1 + -6cos + x = 0

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

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

Reorder the terms:
-1 + 1 + -6cos + x = 0 + 1

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

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

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

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

Simplifying
x = 1 + 6cos
Solution
x = {0, 1 + 6cos}