First, factor an #x# out of each term on the left side of the equation:
#10x^3 - 1x^2 - 2x = 0# becomes:
#x(10x^2 - 1x - 2) = 0#
Next, factor the quadratic on the left side of the equation giving:
#x(5x + 2)(2x - 1) = 0#
Now, solve each term on the left side of the equation for #0#:
Solution 1:
#x = 0#
Solution 2:
#5x + 2 = 0#
#5x + 2 - color(red)(2) = 0 - color(red)(2)#
#5x + 0 = -2#
#5x = -2#
#(5x)/color(red)(5) = -2/color(red)(5)#
#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -2/5#
#x = -2/5#
Solution 3:
#2x - 1 = 0#
#2x - 1 + color(red)(1) = 0 + color(red)(1)#
#2x - 0 = 1#
#2x = 1#
#(2x)/color(red)(2) = 1/color(red)(2)#
#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 1/2#
#x = 1/2#
The solutions are:
#x = 0# and #x = -2/5# and #x = 1/2#
