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

Question 136104: solve for S: s(2s-t)=t^2
Answer by JSmall(7) (Show Source): You can put this solution on YOUR website!
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

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