54*. Given the equations of two planes in normal form. How can we obtain the equation of the set of points that are at equal distances from both planes? (This set is the union of the bisector planes of the dihedral angles between the given planes.)

Given the equations of two planes in normal form. How can we obtain the equation of the set of points that are at equal distances from both planes? (This set is the union of the bisector planes of the dihedral angles between the given planes.)
54. Let's denote the left side of the normal equation of a plane symbolically by the letter $P$ and write the equation itself in the form $P=0$. If $P_{1}$ and $P_{2}$ are the left sides of two normal equations of planes, then the equation $P_{1}=P_{2}$ or $P_{1}-P_{2}=0$ is the equation of the set of points equidistant from the two given planes. This is their bisector plane. The other bisector plane is given by the equation: $P_{1}+P_{2}=0$ (explain!).