(P-6) (3p-21)=0

To solve the equation $(P-6)(3P-21)=0$, we can use the property that if the product of two expressions is zero, then at least one of the expressions must be zero. We can set each expression equal to zero and solve for $P$.

1. Solve $P - 6 = 0$:

$$P - 6 = 0$$ $$P = 6$$

1. Solve $3P - 21 = 0$:

$$3P - 21 = 0$$

Adding 21 to both sides:

$$3P = 21$$

Dividing by 3:

$$P = 7$$

Therefore, the solutions to the equation $(P-6)(3P-21)=0$ are $P = 6$ and $P = 7$.