6x^2-5x-21=(x-7/3)(x+3/2)

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Solution for 6x^2-5x-21=(x-7/3)(x+3/2) equation: 


x in (-oo:+oo)

6*x^2-(5*x)-21 = (x-(7/3))*(x+3/2) // - (x-(7/3))*(x+3/2)

6*x^2-((x-(7/3))*(x+3/2))-(5*x)-21 = 0

6*x^2-((x-7/3)*(x+3/2))-5*x-21 = 0

6*x^2-1*(x-7/3)*(x+3/2)-5*x-21 = 0

6*x^2-1*(x-7/3)*(x+3/2)-5*x-21 = 0

5*x^2+5/6*x-5*x-21+7/2 = 0

5*x^2-25/6*x-21+7/2 = 0

5*x^2-25/6*x-35/2 = 0

5*x^2-25/6*x-35/2 = 0

5*(x^2-5/6*x-7/2) = 0

x^2-5/6*x-7/2 = 0

DELTA = (-5/6)^2-(-7/2*1*4)

DELTA = 529/36

DELTA > 0

x = ((529/36)^(1/2)+5/6)/(1*2) or x = (5/6-(529/36)^(1/2))/(1*2)

x = 7/3 or x = -3/2

5*(x+3/2)*(x-7/3) = 0

5*(x+3/2)*(x-7/3) = 0

( x+3/2 )

x+3/2 = 0 // - 3/2

x = -3/2

( x-7/3 )

x-7/3 = 0 // + 7/3

x = 7/3

x in { -3/2, 7/3 }

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