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The equation can be expressed as ( 15x^2 = 15x ), where ( x ) is the nonzero number. Dividing both sides by 15 (since 15 is nonzero) simplifies to ( x^2 = x ). This implies ( x(x - 1) = 0 ), giving solutions ( x = 0 ) or ( x = 1 ). Since we are looking for a nonzero number, the solution is ( x = 1 ).

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