L[c(t)]=L[5t]

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Solution for L[c(t)]=L[5t] equation: 


Simplifying
L[c(t)] = L[5t]

Multiply c * t
L[ct] = L[5t]

Multiply L * ct
ctL = L[5t]

Remove brackets around [5t]
ctL = L * 5t

Reorder the terms for easier multiplication:
ctL = 5L * t

Multiply L * t
ctL = 5tL

Solving
ctL = 5tL

Solving for variable 'c'.

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

Divide each side by 'tL'.
c = 5

Simplifying
c = 5

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