Question 271999
{{{r^2 -7r -8=0}}}
This is a quadratic equation (because of the {{{r^2}}} term). So we want a zero on one side (which we already have) and then we either factor the other side or use the Quadratic Formula. I prefer factoring when possible and this equation factors fairly easily. As a trinomial with a 1 in front of the squared term, this  can be factored by answering the question: "What factors of the number at the end (-8) that add up to the coefficient in the middle (-7)?" With a little thought and perhaps some trial and error, we should find that the only pair of factors of -8 that add up to -7 are: -8 and 1. So the equation factors into:
{{{(r-8)(r+1) = 0}}}
From the Zero Product Property we know that this product can only be zero if one of the factors is zero. So:
{{{r-8 = 0}}} or {{{r+1 = 0}}}
Solving these we get:
{{{r = 8}}} or {{{r = -1}}}