12+6cosx(2x)=18cos(x)

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Solution for 12+6cosx(2x)=18cos(x) equation:


Simplifying
12 + 6cosx(2x) = 18cos(x)

Remove parenthesis around (2x)
12 + 6cosx * 2x = 18cos(x)

Reorder the terms for easier multiplication:
12 + 6 * 2cosx * x = 18cos(x)

Multiply 6 * 2
12 + 12cosx * x = 18cos(x)

Multiply cosx * x
12 + 12cosx2 = 18cos(x)

Multiply cos * x
12 + 12cosx2 = 18cosx

Solving
12 + 12cosx2 = 18cosx

Solving for variable 'c'.

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

Add '-18cosx' to each side of the equation.
12 + -18cosx + 12cosx2 = 18cosx + -18cosx

Combine like terms: 18cosx + -18cosx = 0
12 + -18cosx + 12cosx2 = 0

Add '-12' to each side of the equation.
12 + -18cosx + -12 + 12cosx2 = 0 + -12

Reorder the terms:
12 + -12 + -18cosx + 12cosx2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -18cosx + 12cosx2 = 0 + -12
-18cosx + 12cosx2 = 0 + -12

Combine like terms: 0 + -12 = -12
-18cosx + 12cosx2 = -12

Reorder the terms:
12 + -18cosx + 12cosx2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + -18cosx + 12cosx2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + -3cosx + 2cosx2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(2 + -3cosx + 2cosx2)' equal to zero and attempt to solve: Simplifying 2 + -3cosx + 2cosx2 = 0 Solving 2 + -3cosx + 2cosx2 = 0 Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -3cosx + -2 + 2cosx2 = 0 + -2 Reorder the terms: 2 + -2 + -3cosx + 2cosx2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3cosx + 2cosx2 = 0 + -2 -3cosx + 2cosx2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3cosx + 2cosx2 = -2 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.

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