How do you solve #15x ^ { 3} - 65x ^ { 2} - 150x = 0#?

1 Answer
Jim G.
May 26, 2017

#x=-5/3,x=0,x=6#

Explanation:

#"take out a "color(blue)"common factor"" of " 5x#

#rArr5x(3x^2-13x-30)=0to(color(magenta)(1))#

#"to factorise the quadratic, 'split' the middle term"#

#rArr3x^2-18x+5x-30#

#"factorise by 'grouping'"#

#color(red)(3x)(x-6)color(red)(+5)(x-6)#

#"take out the comon factor " (x-6)#

#(x-6)(color(red)(3x+5))#

#"returning to " (color(magenta)(1))#

#rArr5x(x-6)(3x+5)=0#

#"equate each factor to zero and solve"#

#5x=0rArrx=0larr" is a solution"#

#x-6=0rArrx=6larr" is a solution"#

#3x+5=0rArrx=-5/3larr" is a solution"#

Related questions
Impact of this question
670 views around the world
You can reuse this answer
Creative Commons License