Question 189076
{{{2x(x+4)(4x-9)=0}}} Start with the given equation.



{{{2x=0}}}, {{{x+4=0}}}, {{{4x-9=0}}} Set each factor equal to zero (use the zero product property)


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Let's solve the first equation:



{{{2x=0}}} Start with the first equation.



{{{x=0/2}}} Divide both sides by 2.



{{{x=0}}} Reduce



So the first solution is {{{x=-4}}}


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Let's solve the second equation:



{{{x+4=0}}} Start with the second equation.



{{{x=-4}}} Subtract 4 from both sides.



So the second solution is {{{x=-4}}}

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Let's solve the third equation:



{{{4x-9=0}}} Start with the third equation.



{{{4x=9}}} Add 9 to both sides.



{{{x=9/4}}} Divide both sides by 4.



So the third solution is {{{x=9/4}}}



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So the three solutions are {{{x=0}}}, {{{x=-4}}}, or {{{x=9/4}}} (note: the order of the solutions does not matter)