cos*5*x*cos*3*x-sin*5*x*sin*3*x=0

Solution for cos*5*x*cos*3*x-sin*5*x*sin*3*x=0 equation:

Simplifying
cos * 5x * cos * 3x + -1sin * 5x * sin * 3x = 0

Reorder the terms for easier multiplication:
5 * 3cos * x * cos * x + -1sin * 5x * sin * 3x = 0

Multiply 5 * 3
15cos * x * cos * x + -1sin * 5x * sin * 3x = 0

Multiply cos * x
15cosx * cos * x + -1sin * 5x * sin * 3x = 0

Multiply cosx * cos
15c2o2s2x * x + -1sin * 5x * sin * 3x = 0

Multiply c2o2s2x * x
15c2o2s2x2 + -1sin * 5x * sin * 3x = 0

Reorder the terms for easier multiplication:
15c2o2s2x2 + -1 * 5 * 3ins * x * ins * x = 0

Multiply -1 * 5
15c2o2s2x2 + -5 * 3ins * x * ins * x = 0

Multiply -5 * 3
15c2o2s2x2 + -15ins * x * ins * x = 0

Multiply ins * x
15c2o2s2x2 + -15insx * ins * x = 0

Multiply insx * ins
15c2o2s2x2 + -15i2n2s2x * x = 0

Multiply i2n2s2x * x
15c2o2s2x2 + -15i2n2s2x2 = 0

Solving
15c2o2s2x2 + -15i2n2s2x2 = 0

Solving for variable 'c'.

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

Add '15i2n2s2x2' to each side of the equation.
15c2o2s2x2 + -15i2n2s2x2 + 15i2n2s2x2 = 0 + 15i2n2s2x2

Combine like terms: -15i2n2s2x2 + 15i2n2s2x2 = 0
15c2o2s2x2 + 0 = 0 + 15i2n2s2x2
15c2o2s2x2 = 0 + 15i2n2s2x2
Remove the zero:
15c2o2s2x2 = 15i2n2s2x2

Divide each side by '15o2s2x2'.
c2 = i2n2o-2

Simplifying
c2 = i2n2o-2

Take the square root of each side:
c = {-1ino-1, ino-1}