# Problem of the Week

## Updated at Aug 23, 2021 5:59 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve $$\frac{{x}^{2}}{5}(5-\frac{5}{x})=6$$?

Check out the solution below!

$\frac{{x}^{2}}{5}(5-\frac{5}{x})=6$

 1 Use this rule: $$\frac{a}{b} \times c=\frac{ac}{b}$$.$\frac{{x}^{2}(5-\frac{5}{x})}{5}=6$2 Factor out the common term $$5$$.$\frac{{x}^{2}\times 5(1-\frac{1}{x})}{5}=6$3 Regroup terms.$\frac{5{x}^{2}(1-\frac{1}{x})}{5}=6$4 Cancel $$5$$.${x}^{2}(1-\frac{1}{x})=6$5 Expand.${x}^{2}-x=6$6 Move all terms to one side.${x}^{2}-x-6=0$7 Factor $${x}^{2}-x-6$$.1 Ask: Which two numbers add up to $$-1$$ and multiply to $$-6$$?$$-3$$ and $$2$$2 Rewrite the expression using the above.$(x-3)(x+2)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$(x-3)(x+2)=0$8 Solve for $$x$$.1 Ask: When will $$(x-3)(x+2)$$ equal zero?When $$x-3=0$$ or $$x+2=0$$2 Solve each of the 2 equations above.$x=3,-2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$x=3,-2$Donex=3,-2