F(x)=5cos^2(x)-10sin(x)

Solution for F(x)=5cos^2(x)-10sin(x) equation:

Simplifying
F(x) = 5cos2(x) + -10sin(x)

Multiply F * x
xF = 5cos2(x) + -10sin(x)

Multiply cos2 * x
xF = 5cos2x + -10sin(x)

Multiply ins * x
xF = 5cos2x + -10insx

Solving
xF = 5cos2x + -10insx

Solving for variable 'x'.

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

Add '-5cos2x' to each side of the equation.
-5cos2x + xF = 5cos2x + -5cos2x + -10insx

Combine like terms: 5cos2x + -5cos2x = 0
-5cos2x + xF = 0 + -10insx
-5cos2x + xF = -10insx

Add '10insx' to each side of the equation.
-5cos2x + 10insx + xF = -10insx + 10insx

Combine like terms: -10insx + 10insx = 0
-5cos2x + 10insx + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5cos2 + 10ins + F) = 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 '(-5cos2 + 10ins + F)' equal to zero and attempt to solve:

Simplifying
-5cos2 + 10ins + F = 0

Reorder the terms:
F + -5cos2 + 10ins = 0

Solving
F + -5cos2 + 10ins = 0

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

Add '-1F' to each side of the equation.
F + -5cos2 + -1F + 10ins = 0 + -1F

Reorder the terms:
F + -1F + -5cos2 + 10ins = 0 + -1F

Combine like terms: F + -1F = 0
0 + -5cos2 + 10ins = 0 + -1F
-5cos2 + 10ins = 0 + -1F
Remove the zero:
-5cos2 + 10ins = -1F

Add '5cos2' to each side of the equation.
-5cos2 + 5cos2 + 10ins = -1F + 5cos2

Combine like terms: -5cos2 + 5cos2 = 0
0 + 10ins = -1F + 5cos2
10ins = -1F + 5cos2

Add '-10ins' to each side of the equation.
10ins + -10ins = -1F + 5cos2 + -10ins

Combine like terms: 10ins + -10ins = 0
0 = -1F + 5cos2 + -10ins

Simplifying
0 = -1F + 5cos2 + -10ins

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}