Question 297091
16r^3 - 9r = 0


Factor out the r on the left side of the equation to get


r * (16r^2 - 9) = 0


r = 0 will satisfy this equation because anything times 0 equals 0.


16r^2 - 9 = 0 will also satisfy this equation because anything times 0 equals 0.


Solve for 16r^2 - 9 = 0


Add 9 to both sides of this equation to get 16r^2 = 9


Divide both sides of this equation by 16 to get r^2 = (9/16)


Take the square root of both sides of this equation to get r = +/- sqrt(9/16)


Since sqrt(9/16) is the same as sqrt(9) / sqrt(16), and since sqrt(9) = 3, and since sqrt(16) = 4, you get r  = +/- 3/4


You have 3 possible answers to this equation.


They are:


r = 0
r = 3/4
r = -3/4


Plug those values into the original equation to see if they hold up.


Your original equation is 16r^3 - 9r = 0


When r = 0, this equation becomes 0 - 0 = 0 which is true.


When r = 3/4, this equation becomes 16*27/64 - 9*3/4 = 432/64 - 27/4 = 6.75 - 6.75 = 0 which is true.


When r = -3/4, this equation becomes 16*-27/64 + 9*3/4 = -432/64 + 27/4 = -6.75 + 6.75 = 0 which is true.


All 3 answers are solutions to the original equation.