Question 257597
3x(2x-5)(3x+1)=0 

If any individual factor on the left-hand side of the equation is equal to 0, the entire expression will be equal to 0. 

3x=0 
(2x-5)=0 
(3x+1)=0 


Set the first factor equal to 0 and solve. 

3x=0 


Divide each term in the equation by 3. 

 3x/3=0/3


Simplify the left-hand side of the equation by canceling the common factors. 

 x=0/3


0 divided by any number or variable is 0. 

x=0 


Set the next factor equal to 0 and solve. 

(2x-5)=0 


Remove the parentheses around the expression 2x-5. 

2x-5=0 


Since -5 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 5 to both sides. 

2x=5 


Divide each term in the equation by 2. 

 2x/2=5/2


Simplify the left-hand side of the equation by canceling the common factors. 

 x=5/2


Set the next factor equal to 0 and solve. 

(3x+1)=0 


Remove the parentheses around the expression 3x+1. 

3x+1=0 


Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides. 

3x=-1 


Divide each term in the equation by 3. 

 3x/3=-1/3


Simplify the left-hand side of the equation by canceling the common factors. 

 x=-1/3


The final solution is all the values that make 3x(2x-5)(3x+1)=0 true. 

 Answer:  x=0, 5/2, -1/3