Question 136104
solve for S: s(2s-t)=t^2

This solution will be:
1) Simplify the left side
2) Get one side of the equation equal to zero.
3) Factor the other side
4) Set each factor to zero and solve.

1) Simplify
  s(2s-t) = t^2
using the Distributive Proporty
  2s^2 - st = t^2
2) Get one side equal to zero by subtracting t^2 from each side:
  2s^2 - st - t^2  = t^2 - t^2
which simplifies to
  2s^2 - st - t^2  = 0
3) Factor the left side. (Unfortunately there is not enough time and space for me to explain all the details of factoring. I hope that when you see how it factors you will understand.)
  (2s + t) (s - t) = 0
4) Set each factor to zero. (The only way for a product (multiplication) to result in zero is if one of the factors is zero.) So
  2s + t = 0
or
  s - t = 0
5) Solve each equation
  2s + t = 0
Subtract t from each side
  2s = -t
Divide each side by two
  s = -t/2

For the equation s - t = 0 add t to both sides resulting in:
  s = t

So the solution is
  s = -t/2 or s = t