# Problem of the Week

## Updated at Feb 11, 2019 4:37 PM

How would you solve the equation $$(4+4m)\times \frac{3-m}{5}=\frac{12}{5}$$?

Below is the solution.

$(4+4m)\times \frac{3-m}{5}=\frac{12}{5}$

 1 Use this rule: $$a \times \frac{b}{c}=\frac{ab}{c}$$.$\frac{(4+4m)(3-m)}{5}=\frac{12}{5}$2 Factor out the common term $$4$$.$\frac{4(1+m)(3-m)}{5}=\frac{12}{5}$3 Multiply both sides by $$5$$.$4(1+m)(3-m)=12$4 Expand.$12-4m+12m-4{m}^{2}=12$5 Simplify  $$12-4m+12m-4{m}^{2}$$  to  $$12+8m-4{m}^{2}$$.$12+8m-4{m}^{2}=12$6 Cancel $$12$$ on both sides.$8m-4{m}^{2}=0$7 Factor out the common term $$4m$$.$4m(2-m)=0$8 Solve for $$m$$.1 Ask: When will $$m(2-m)$$ equal zero?When $$m=0$$ or $$2-m=0$$2 Solve each of the 2 equations above.$m=0,2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$m=0,2$Donem=0,2