Two small charged spheres of +25 nC and +16 nC are 0.90 m apart in air…

Step 1. Like charges. Let $x$ be the distance from the $25$ nC sphere. The fields cancel when $\dfrac{k \times 25}{x^2} = \dfrac{k \times 16}{(0.90 - x)^2}$. So $\dfrac{x}{0.90 - x} = \sqrt{\dfrac{25}{16}} = \dfrac{5}{4}$. We want $x$, so $x = \dfrac{5}{9} \times 0.90\ \text{m} = 0.50\ \text{m}$.

Step 2. Opposite charges. Between the spheres the two fields point the same way, so there is no zero there. Take a point beyond the $-16$ nC sphere, at a distance $y$ from it. The field of the $+25$ nC sphere points away from that sphere. The field of the $-16$ nC sphere points towards it. So they can cancel. Equal sizes give $\dfrac{0.90 + y}{y} = \dfrac{5}{4}$. So $0.90 + y = 1.25y$, and $y = \dfrac{0.90}{0.25}\ \text{m} = 3.6\ \text{m}$.