please help meX(x-4)(3x+2)=240 find the value of X

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malagala | College Teacher | (Level 2) Adjunct Educator

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first we have to rearrange the equation as follows,

X(x-4)(3x+2)=240

=>x(3x^2 - 10x -8) - 240 = 0

=> 3x^3 - 10x^2 -8x -240 = 0 -----(1)

when we consider the equation (1)

when x = 6, LHS = 0

hence x = 6 is a solution in this equation,

therefore equation (1) can be rewritten as,

3x^3 - 10x^2 -8x -240 = 0 

=>(x-6)(3x^2 +8x +40) = 0

in order to satisfy this condition,

x = 6 or 3x^2 +8x +40 = 0

now this has become a second degree equation solution,

3x^2 +8x +40 = 0

solutions of this equations are,

x = (-4 +sqrt(-104))/3 and x= (-4 -sqrt(-104))/3

hence the solutions for this question are,

x= 6

x = (-4 +sqrt(-104))/3 = (-4 + 10.2i)/3

x= (-4 -sqrt(-104))/3 = (-4 - 10.2i)/3

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