Question 69073
You can use the technique of factoring by grouping to solve this problem.
{{{9x^3 - 18x^2 - 4x + 8 = 0}}} Group the terms as follows:
{{{(9x^3 - 18x^2) - (4x - 8) = 0}}} Notice the change in sign of the last term. Factor {{{9x^2}}} from the first group and factor {{{4}}} from the second group:
{{{9x^2(x - 2) - 4(x - 2) = 0}}} Now you can factor the common term (x - 2).
{{{(x - 2)(9x^2-4) = 0}}} Apply the zero product principle.
{{{x-2) = 0}}} and/or {{{9x^2-4 = 0}}}
If {{{x-2 = 0}}} then {{{x = 2}}}
If {{{9x^2-4 = 0}}} then {{{9x^2 = 4}}} and so {{{x^2 = 4/9}}} and {{{x = 2/3}}} or {{{x = -2/3}}}
Solutions:
{{{x = 2}}}
{{{x = 2/3}}}
{{{x = -2/3}}}