(cosx-1)(cosx-4)=0

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Solution for (cosx-1)(cosx-4)=0 equation: 


Simplifying
(cosx + -1)(cosx + -4) = 0

Reorder the terms:
(-1 + cosx)(cosx + -4) = 0

Reorder the terms:
(-1 + cosx)(-4 + cosx) = 0

Multiply (-1 + cosx) * (-4 + cosx)
(-1(-4 + cosx) + cosx(-4 + cosx)) = 0
((-4 * -1 + cosx * -1) + cosx(-4 + cosx)) = 0
((4 + -1cosx) + cosx(-4 + cosx)) = 0
(4 + -1cosx + (-4 * cosx + cosx * cosx)) = 0
(4 + -1cosx + (-4cosx + c2o2s2x2)) = 0

Combine like terms: -1cosx + -4cosx = -5cosx
(4 + -5cosx + c2o2s2x2) = 0

Solving
4 + -5cosx + c2o2s2x2 = 0

Solving for variable 'c'.

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


Subproblem 1
Set the factor '(1 + -1cosx)' equal to zero and attempt to solve:

Simplifying
1 + -1cosx = 0

Solving
1 + -1cosx = 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 + -1cosx = 0 + -1

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

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

Divide each side by '-1osx'.
c = o-1s-1x-1

Simplifying
c = o-1s-1x-1

Subproblem 2
Set the factor '(4 + -1cosx)' equal to zero and attempt to solve:

Simplifying
4 + -1cosx = 0

Solving
4 + -1cosx = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1cosx = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1cosx = 0 + -4
-1cosx = 0 + -4

Combine like terms: 0 + -4 = -4
-1cosx = -4

Divide each side by '-1osx'.
c = 4o-1s-1x-1

Simplifying
c = 4o-1s-1x-1
Solution
c = {o-1s-1x-1, 4o-1s-1x-1}

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