Solving a hard algebraic equation

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The question is:

Rectangular floor mats have an area of $x^2 + 2x - 15 \text{ cm}^2$. The length is $x + 5\text{ cm}$, and the width is $100\text{ cm}$. How do I find out the value of $x$, and from there the length of the mat? The equation to find the width is $$\frac{x^2+2x-15}{\text{length}}$$

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1 Answer

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Hint. One may solve, for $x>0$, $$ \frac{x^2+2x-15}{x+5}=100 $$ or $$ \frac{(x+5)(x-3)}{x+5}=100 $$

Can you take it from here?

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