Solve rational equation. 2−3y=5y2

Step 1
LCD is ${\displaystyle y^2}$
We multiply both sides by LCD and distribute it
${\displaystyle 2-\frac{3}{y}=\frac{5}{y^2}}$
Or, ${\displaystyle y^2(2-\frac{3}{y})=y^2\frac{5}{y^2}}$
Or, ${\displaystyle 2y^2-3y=5}$
Step 2
Make right side equal to 0 and factor the left side
${\displaystyle 2y^2-3y=5}$
Or, ${\displaystyle 2y^2-3y-5=0}$
Or, ${\displaystyle 2y^2-5y+2y-5=0}$
Or, y(2y-5)+1(2y-5)=0
Or, (2y-5)(y+1)=0
Step 3
Set each factor equal to 0 and find y.
Answer: $y=\frac{5}{2}$ or -1
2y-5=0
Or, 2y=5
Or, ${\displaystyle y=\frac{5}{2}}$
y+1=0
Or, y=-1