x=sin(5x)cos(2x)+cos(5x)sin(2x)

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Solution for x=sin(5x)cos(2x)+cos(5x)sin(2x) equation: 


Simplifying
x = sin(5x) * cos(2x) + cos(5x) * sin(2x)

Remove parenthesis around (5x)
x = ins * 5x * cos(2x) + cos(5x) * sin(2x)

Remove parenthesis around (2x)
x = ins * 5x * cos * 2x + cos(5x) * sin(2x)

Reorder the terms for easier multiplication:
x = 5 * 2ins * x * cos * x + cos(5x) * sin(2x)

Multiply 5 * 2
x = 10ins * x * cos * x + cos(5x) * sin(2x)

Multiply ins * x
x = 10insx * cos * x + cos(5x) * sin(2x)

Multiply insx * cos
x = 10cinos2x * x + cos(5x) * sin(2x)

Multiply cinos2x * x
x = 10cinos2x2 + cos(5x) * sin(2x)

Remove parenthesis around (5x)
x = 10cinos2x2 + cos * 5x * sin(2x)

Remove parenthesis around (2x)
x = 10cinos2x2 + cos * 5x * ins * 2x

Reorder the terms for easier multiplication:
x = 10cinos2x2 + 5 * 2cos * x * ins * x

Multiply 5 * 2
x = 10cinos2x2 + 10cos * x * ins * x

Multiply cos * x
x = 10cinos2x2 + 10cosx * ins * x

Multiply cosx * ins
x = 10cinos2x2 + 10cinos2x * x

Multiply cinos2x * x
x = 10cinos2x2 + 10cinos2x2

Combine like terms: 10cinos2x2 + 10cinos2x2 = 20cinos2x2
x = 20cinos2x2

Solving
x = 20cinos2x2

Solving for variable 'x'.

Reorder the terms:
-20cinos2x2 + x = 20cinos2x2 + -20cinos2x2

Combine like terms: 20cinos2x2 + -20cinos2x2 = 0
-20cinos2x2 + x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-20cinos2x + 1) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-20cinos2x + 1)' equal to zero and attempt to solve:

Simplifying
-20cinos2x + 1 = 0

Reorder the terms:
1 + -20cinos2x = 0

Solving
1 + -20cinos2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -20cinos2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -20cinos2x = 0 + -1
-20cinos2x = 0 + -1

Combine like terms: 0 + -1 = -1
-20cinos2x = -1

Divide each side by '-20cinos2'.
x = 0.05c-1i-1n-1o-1s-2

Simplifying
x = 0.05c-1i-1n-1o-1s-2
Solution
x = {0, 0.05c-1i-1n-1o-1s-2}

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