(4t^2-4/9(t+1)^2)(3t+3/2t-2)

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Solution for (4t^2-4/9(t+1)^2)(3t+3/2t-2) equation:


t in (-oo:+oo)

(4*t^2-((4/9)*(t+1)^2))*(3*t+(3/2)*t-2) = 0

((-4/9)*(t+1)^2+4*t^2)*(3*t+(3/2)*t-2) = 0

(9/2*t-2)*(4*t^2-4/9*(t+1)^2) = 0

4*t^2-4/9*(t+1)^2 = 0

4*t^2-4/9*(t+1)^2 = 0

32/9*t^2-8/9*t-4/9 = 0

32/9*t^2-8/9*t-4/9 = 0

4/9*(8*t^2-2*t-1) = 0

8*t^2-2*t-1 = 0

DELTA = (-2)^2-(-1*4*8)

DELTA = 36

DELTA > 0

t = (36^(1/2)+2)/(2*8) or t = (2-36^(1/2))/(2*8)

t = 1/2 or t = -1/4

4/9*(t+1/4)*(t-1/2) = 0

4/9*(t+1/4)*(t-1/2) = 0

4/9*(9/2*t-2)*(t+1/4)*(t-1/2) = 0

( 9/2*t-2 )

9/2*t-2 = 0 // + 2

9/2*t = 2 // : 9/2

t = 2/9/2

t = 4/9

( t+1/4 )

t+1/4 = 0 // - 1/4

t = -1/4

( t-1/2 )

t-1/2 = 0 // + 1/2

t = 1/2

t in { 4/9, -1/4, 1/2 }

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