cos(4x)cos(x)+sin(4x)sin(x)=-.5

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Solution for cos(4x)cos(x)+sin(4x)sin(x)=-.5 equation: 


Simplifying
cos(4x) * cos(x) + sin(4x) * sin(x) = -0.5

Remove parenthesis around (4x)
cos * 4x * cos(x) + sin(4x) * sin(x) = -0.5

Reorder the terms for easier multiplication:
4cos * x * cos * x + sin(4x) * sin(x) = -0.5

Multiply cos * x
4cosx * cos * x + sin(4x) * sin(x) = -0.5

Multiply cosx * cos
4c2o2s2x * x + sin(4x) * sin(x) = -0.5

Multiply c2o2s2x * x
4c2o2s2x2 + sin(4x) * sin(x) = -0.5

Remove parenthesis around (4x)
4c2o2s2x2 + ins * 4x * sin(x) = -0.5

Reorder the terms for easier multiplication:
4c2o2s2x2 + 4ins * x * ins * x = -0.5

Multiply ins * x
4c2o2s2x2 + 4insx * ins * x = -0.5

Multiply insx * ins
4c2o2s2x2 + 4i2n2s2x * x = -0.5

Multiply i2n2s2x * x
4c2o2s2x2 + 4i2n2s2x2 = -0.5

Solving
4c2o2s2x2 + 4i2n2s2x2 = -0.5

Solving for variable 'c'.

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

Add '-4i2n2s2x2' to each side of the equation.
4c2o2s2x2 + 4i2n2s2x2 + -4i2n2s2x2 = -0.5 + -4i2n2s2x2

Combine like terms: 4i2n2s2x2 + -4i2n2s2x2 = 0
4c2o2s2x2 + 0 = -0.5 + -4i2n2s2x2
4c2o2s2x2 = -0.5 + -4i2n2s2x2

Divide each side by '4o2s2x2'.
c2 = -0.125o-2s-2x-2 + -1i2n2o-2

Simplifying
c2 = -0.125o-2s-2x-2 + -1i2n2o-2

Reorder the terms:
c2 = -1i2n2o-2 + -0.125o-2s-2x-2

Reorder the terms:
c2 + i2n2o-2 + 0.125o-2s-2x-2 = -1i2n2o-2 + i2n2o-2 + -0.125o-2s-2x-2 + 0.125o-2s-2x-2

Combine like terms: -1i2n2o-2 + i2n2o-2 = 0
c2 + i2n2o-2 + 0.125o-2s-2x-2 = 0 + -0.125o-2s-2x-2 + 0.125o-2s-2x-2
c2 + i2n2o-2 + 0.125o-2s-2x-2 = -0.125o-2s-2x-2 + 0.125o-2s-2x-2

Combine like terms: -0.125o-2s-2x-2 + 0.125o-2s-2x-2 = 0.000
c2 + i2n2o-2 + 0.125o-2s-2x-2 = 0.000

The solution to this equation could not be determined.

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