(cos(x)-1)(cos(x)-8)=0

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Solution for (cos(x)-1)(cos(x)-8)=0 equation: 


Simplifying
(cos(x) + -1)(cos(x) + -8) = 0

Multiply cos * x
(cosx + -1)(cos(x) + -8) = 0

Reorder the terms:
(-1 + cosx)(cos(x) + -8) = 0

Multiply cos * x
(-1 + cosx)(cosx + -8) = 0

Reorder the terms:
(-1 + cosx)(-8 + cosx) = 0

Multiply (-1 + cosx) * (-8 + cosx)
(-1(-8 + cosx) + cosx(-8 + cosx)) = 0
((-8 * -1 + cosx * -1) + cosx(-8 + cosx)) = 0
((8 + -1cosx) + cosx(-8 + cosx)) = 0
(8 + -1cosx + (-8 * cosx + cosx * cosx)) = 0
(8 + -1cosx + (-8cosx + c2o2s2x2)) = 0

Combine like terms: -1cosx + -8cosx = -9cosx
(8 + -9cosx + c2o2s2x2) = 0

Solving
8 + -9cosx + c2o2s2x2 = 0

Solving for variable 'c'.

Factor a trinomial.
(1 + -1cosx)(8 + -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 '(8 + -1cosx)' equal to zero and attempt to solve:

Simplifying
8 + -1cosx = 0

Solving
8 + -1cosx = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1cosx = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1cosx = 0 + -8
-1cosx = 0 + -8

Combine like terms: 0 + -8 = -8
-1cosx = -8

Divide each side by '-1osx'.
c = 8o-1s-1x-1

Simplifying
c = 8o-1s-1x-1
Solution
c = {o-1s-1x-1, 8o-1s-1x-1}

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