L(t)=30sin(t)-20cos(t)

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Solution for L(t)=30sin(t)-20cos(t) equation: 


Simplifying
L(t) = 30sin(t) + -20cos(t)

Multiply L * t
tL = 30sin(t) + -20cos(t)

Multiply ins * t
tL = 30inst + -20cos(t)

Multiply cos * t
tL = 30inst + -20cost

Reorder the terms:
tL = -20cost + 30inst

Solving
tL = -20cost + 30inst

Solving for variable 't'.

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

Add '20cost' to each side of the equation.
20cost + tL = -20cost + 20cost + 30inst

Combine like terms: -20cost + 20cost = 0
20cost + tL = 0 + 30inst
20cost + tL = 30inst

Add '-30inst' to each side of the equation.
20cost + -30inst + tL = 30inst + -30inst

Combine like terms: 30inst + -30inst = 0
20cost + -30inst + tL = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(20cos + -30ins + L) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0

Subproblem 2
Set the factor '(20cos + -30ins + L)' equal to zero and attempt to solve:

Simplifying
20cos + -30ins + L = 0

Reorder the terms:
L + 20cos + -30ins = 0

Solving
L + 20cos + -30ins = 0

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

Add '-1L' to each side of the equation.
L + 20cos + -1L + -30ins = 0 + -1L

Reorder the terms:
L + -1L + 20cos + -30ins = 0 + -1L

Combine like terms: L + -1L = 0
0 + 20cos + -30ins = 0 + -1L
20cos + -30ins = 0 + -1L
Remove the zero:
20cos + -30ins = -1L

Add '-20cos' to each side of the equation.
20cos + -20cos + -30ins = -1L + -20cos

Combine like terms: 20cos + -20cos = 0
0 + -30ins = -1L + -20cos
-30ins = -1L + -20cos

Add '30ins' to each side of the equation.
-30ins + 30ins = -1L + -20cos + 30ins

Combine like terms: -30ins + 30ins = 0
0 = -1L + -20cos + 30ins

Simplifying
0 = -1L + -20cos + 30ins

The solution to this equation could not be determined.

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

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