# How do you solve 25a=10a^2?

Apr 24, 2018

$\implies a = \frac{5}{2}$

#### Explanation:

We are given

$25 a = 10 {a}^{2}$

First we divide both sides by $a$:

$\frac{25 \cancel{a}}{\cancel{a}} = \frac{10 {a}^{\cancel{2}}}{\cancel{a}}$

$25 = 10 a$

Then we divide both sides by $10$:

$\frac{25}{10} = \frac{\cancel{10} a}{\cancel{10}}$

$\frac{5}{2} = a$

Apr 24, 2018

$a = 0 , \frac{5}{2}$

#### Explanation:

We can start by subtracting $25 a$ from both sides to get

$10 {a}^{2} - 25 a = 0$

We can factor out a $5 a$ to get

$5 a \left(2 a - 5\right) = 0$

We now set both factors equal to zero:

$5 a = 0 \implies \textcolor{b l u e}{a = 0}$

$2 a - 5 = 0 \implies 2 a = 5 \implies \textcolor{b l u e}{a = \frac{5}{2}}$

Hope this helps!