(3+5cosx)(3-5cosx)=25sin^2x-16

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Solution for (3+5cosx)(3-5cosx)=25sin^2x-16 equation: 


Simplifying
(3 + 5cosx)(3 + -5cosx) = 25sin2x + -16

Multiply (3 + 5cosx) * (3 + -5cosx)
(3(3 + -5cosx) + 5cosx * (3 + -5cosx)) = 25sin2x + -16
((3 * 3 + -5cosx * 3) + 5cosx * (3 + -5cosx)) = 25sin2x + -16
((9 + -15cosx) + 5cosx * (3 + -5cosx)) = 25sin2x + -16
(9 + -15cosx + (3 * 5cosx + -5cosx * 5cosx)) = 25sin2x + -16
(9 + -15cosx + (15cosx + -25c2o2s2x2)) = 25sin2x + -16

Combine like terms: -15cosx + 15cosx = 0
(9 + 0 + -25c2o2s2x2) = 25sin2x + -16
(9 + -25c2o2s2x2) = 25sin2x + -16

Reorder the terms:
9 + -25c2o2s2x2 = -16 + 25in2sx

Solving
9 + -25c2o2s2x2 = -16 + 25in2sx

Solving for variable 'c'.

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

Add '-9' to each side of the equation.
9 + -9 + -25c2o2s2x2 = -16 + -9 + 25in2sx

Combine like terms: 9 + -9 = 0
0 + -25c2o2s2x2 = -16 + -9 + 25in2sx
-25c2o2s2x2 = -16 + -9 + 25in2sx

Combine like terms: -16 + -9 = -25
-25c2o2s2x2 = -25 + 25in2sx

Divide each side by '-25o2s2x2'.
c2 = o-2s-2x-2 + -1in2o-2s-1x-1

Simplifying
c2 = o-2s-2x-2 + -1in2o-2s-1x-1

Reorder the terms:
c2 = -1in2o-2s-1x-1 + o-2s-2x-2

Reorder the terms:
c2 + in2o-2s-1x-1 + -1o-2s-2x-2 = -1in2o-2s-1x-1 + in2o-2s-1x-1 + o-2s-2x-2 + -1o-2s-2x-2

Combine like terms: -1in2o-2s-1x-1 + in2o-2s-1x-1 = 0
c2 + in2o-2s-1x-1 + -1o-2s-2x-2 = 0 + o-2s-2x-2 + -1o-2s-2x-2
c2 + in2o-2s-1x-1 + -1o-2s-2x-2 = o-2s-2x-2 + -1o-2s-2x-2

Combine like terms: o-2s-2x-2 + -1o-2s-2x-2 = 0
c2 + in2o-2s-1x-1 + -1o-2s-2x-2 = 0

The solution to this equation could not be determined.

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