2sec(x+60)=5sec(x-20)

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Solution for 2sec(x+60)=5sec(x-20) equation: 


Simplifying
2sec(x + 60) = 5sec(x + -20)

Reorder the terms:
2ces(60 + x) = 5sec(x + -20)
(60 * 2ces + x * 2ces) = 5sec(x + -20)
(120ces + 2cesx) = 5sec(x + -20)

Reorder the terms:
120ces + 2cesx = 5ces(-20 + x)
120ces + 2cesx = (-20 * 5ces + x * 5ces)
120ces + 2cesx = (-100ces + 5cesx)

Solving
120ces + 2cesx = -100ces + 5cesx

Solving for variable 'c'.

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

Add '100ces' to each side of the equation.
120ces + 100ces + 2cesx = -100ces + 100ces + 5cesx

Combine like terms: 120ces + 100ces = 220ces
220ces + 2cesx = -100ces + 100ces + 5cesx

Combine like terms: -100ces + 100ces = 0
220ces + 2cesx = 0 + 5cesx
220ces + 2cesx = 5cesx

Add '-5cesx' to each side of the equation.
220ces + 2cesx + -5cesx = 5cesx + -5cesx

Combine like terms: 2cesx + -5cesx = -3cesx
220ces + -3cesx = 5cesx + -5cesx

Combine like terms: 5cesx + -5cesx = 0
220ces + -3cesx = 0

Factor out the Greatest Common Factor (GCF), 'ces'.
ces(220 + -3x) = 0


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

Simplifying
ces = 0

Solving
ces = 0

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

Simplifying
ces = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(220 + -3x)' equal to zero and attempt to solve:

Simplifying
220 + -3x = 0

Solving
220 + -3x = 0

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

Add '-220' to each side of the equation.
220 + -220 + -3x = 0 + -220

Combine like terms: 220 + -220 = 0
0 + -3x = 0 + -220
-3x = 0 + -220

Combine like terms: 0 + -220 = -220
-3x = -220

Add '3x' to each side of the equation.
-3x + 3x = -220 + 3x

Combine like terms: -3x + 3x = 0
0 = -220 + 3x

Simplifying
0 = -220 + 3x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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