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21\left(-2\right)y+10y=0
Multiply both sides of the equation by 10, the least common multiple of 2,5.
-42y+10y=0
Multiply 21 and -2 to get -42.
-32y=0
Combine -42y and 10y to get -32y.
y=0
Product of two numbers is equal to 0 if at least one of them is 0. Since -32 is not equal to 0, y must be equal to 0.