Use a calculator

I think you have:

10e^(-5t) - 50te^(-5t) = 0

(parenthesis around the exponent, not the "e", otherwise you just have t times e to the -5 power, which isn't what I think you want)

To solve this, let's start with moving the second term to the other side:

10e^(-5t) = 50te^(-5t)

Now let's divide both sides by 10:

e^(-5t) = 5te^(-5t)

When we have an equation like:

x = x²

We don't want to just divide both sides by x, since x can equal zero and you can't divide by zero. So doing so you lose a solution:

1 = x

vs. x being 0 or 1 if solved properly.

But here, e^(-5t) can never be zero, so it is safe to divide both sides by this expression. Doing so results in:

1 = 5t

so the solution is:

t = 1/5

As a test, let's substitute that into the original equation and make sure it gets to zero (or close to it due to rounding errors):

10e^(-5t) - 50te^(-5t) = 0

10e^(-5/5) - (50/5)e^(-5/5) = 0

10e^(-1) - 10e^(-1) = 0

10/e - 10/e = 0

0 = 0

It works out, so again we have:

t = 1/5

i need steps please

BTW i know t=0.2

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