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365x+1-365\times 0\times 2\left(365x+1\right)=1
Variable x cannot be equal to -\frac{1}{365} since division by zero is not defined. Multiply both sides of the equation by 365x+1.
365x+1-0\times 2\left(365x+1\right)=1
Multiply 365 and 0 to get 0.
365x+1-0\left(365x+1\right)=1
Multiply 0 and 2 to get 0.
365x+1-0=1
Anything times zero gives zero.
365x+1=1+0
Add 0 to both sides.
365x+1=1
Add 1 and 0 to get 1.
365x=1-1
Subtract 1 from both sides.
365x=0
Subtract 1 from 1 to get 0.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since 365 is not equal to 0, x must be equal to 0.