(6cosx)(6cosx)+3cosx-3=0

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Solution for (6cosx)(6cosx)+3cosx-3=0 equation:


Simplifying
(6cosx)(6cosx) + 3cosx + -3 = 0

Remove parenthesis around (6cosx)
6cosx(6cosx) + 3cosx + -3 = 0

Remove parenthesis around (6cosx)
6cosx * 6cosx + 3cosx + -3 = 0

Reorder the terms for easier multiplication:
6 * 6cosx * cosx + 3cosx + -3 = 0

Multiply 6 * 6
36cosx * cosx + 3cosx + -3 = 0

Multiply cosx * cosx
36c2o2s2x2 + 3cosx + -3 = 0

Reorder the terms:
-3 + 3cosx + 36c2o2s2x2 = 0

Solving
-3 + 3cosx + 36c2o2s2x2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + cosx + 12c2o2s2x2) = 0

Factor a trinomial.
3((-1 + -3cosx)(1 + -4cosx)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + -3cosx)' equal to zero and attempt to solve: Simplifying -1 + -3cosx = 0 Solving -1 + -3cosx = 0 Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3cosx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3cosx = 0 + 1 -3cosx = 0 + 1 Combine like terms: 0 + 1 = 1 -3cosx = 1 Divide each side by '-3osx'. c = -0.3333333333o-1s-1x-1 Simplifying c = -0.3333333333o-1s-1x-1

Subproblem 2

Set the factor '(1 + -4cosx)' equal to zero and attempt to solve: Simplifying 1 + -4cosx = 0 Solving 1 + -4cosx = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4cosx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4cosx = 0 + -1 -4cosx = 0 + -1 Combine like terms: 0 + -1 = -1 -4cosx = -1 Divide each side by '-4osx'. c = 0.25o-1s-1x-1 Simplifying c = 0.25o-1s-1x-1

Solution

c = {-0.3333333333o-1s-1x-1, 0.25o-1s-1x-1}

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