(5sinx+1)(3cosx-1)=0

Solution for (5sinx+1)(3cosx-1)=0 equation:

Simplifying
(5sinx + 1)(3cosx + -1) = 0

Reorder the terms:
(1 + 5insx)(3cosx + -1) = 0

Reorder the terms:
(1 + 5insx)(-1 + 3cosx) = 0

Multiply (1 + 5insx) * (-1 + 3cosx)
(1(-1 + 3cosx) + 5insx * (-1 + 3cosx)) = 0
((-1 * 1 + 3cosx * 1) + 5insx * (-1 + 3cosx)) = 0
((-1 + 3cosx) + 5insx * (-1 + 3cosx)) = 0
(-1 + 3cosx + (-1 * 5insx + 3cosx * 5insx)) = 0

Reorder the terms:
(-1 + 3cosx + (15cinos2x2 + -5insx)) = 0
(-1 + 3cosx + (15cinos2x2 + -5insx)) = 0

Reorder the terms:
(-1 + 15cinos2x2 + 3cosx + -5insx) = 0
(-1 + 15cinos2x2 + 3cosx + -5insx) = 0

Solving
-1 + 15cinos2x2 + 3cosx + -5insx = 0

Solving for variable 'c'.

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

Add '1' to each side of the equation.
-1 + 15cinos2x2 + 3cosx + 1 + -5insx = 0 + 1

Reorder the terms:
-1 + 1 + 15cinos2x2 + 3cosx + -5insx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 15cinos2x2 + 3cosx + -5insx = 0 + 1
15cinos2x2 + 3cosx + -5insx = 0 + 1

Combine like terms: 0 + 1 = 1
15cinos2x2 + 3cosx + -5insx = 1

Add '5insx' to each side of the equation.
15cinos2x2 + 3cosx + -5insx + 5insx = 1 + 5insx

Combine like terms: -5insx + 5insx = 0
15cinos2x2 + 3cosx + 0 = 1 + 5insx
15cinos2x2 + 3cosx = 1 + 5insx

Reorder the terms:
-1 + 15cinos2x2 + 3cosx + -5insx = 1 + 5insx + -1 + -5insx

Reorder the terms:
-1 + 15cinos2x2 + 3cosx + -5insx = 1 + -1 + 5insx + -5insx

Combine like terms: 1 + -1 = 0
-1 + 15cinos2x2 + 3cosx + -5insx = 0 + 5insx + -5insx
-1 + 15cinos2x2 + 3cosx + -5insx = 5insx + -5insx

Combine like terms: 5insx + -5insx = 0
-1 + 15cinos2x2 + 3cosx + -5insx = 0

The solution to this equation could not be determined.