abs(x)abs(x-3)=4abs(x-3/2)

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Solution for abs(x)abs(x-3)=4abs(x-3/2) equation: 


x in (-oo:+oo)

abs(x)*abs(x-3) = 4*abs(x-(3/2)) // - 4*abs(x-(3/2))

abs(x)*abs(x-3)-(4*abs(x-(3/2))) = 0

abs(x)*abs(x-3)-4*abs(x-3/2) = 0

abs(x)*abs(x-3)-4*abs(x-3/2) = 0

x in (-oo:+oo)

abs(x)

x in <0:+oo)

x*abs(x-3)-4*abs(x-3/2) = 0

x in (-oo:0)

-x*abs(x-3)-4*abs(x-3/2) = 0

-x*abs(x-3)-4*abs(x-3/2) = 0

x in (-oo:0)

abs(x-3)

x-3 >= 0

x-3 >= 0 // + 3

x >= 3

x in (-oo:0)

-x*(-(x-3))-4*abs(x-3/2) = 0

x*abs(x-3)-4*abs(x-3/2) = 0

x in <0:+oo)

abs(x-3)

x-3 >= 0

x-3 >= 0 // + 3

x >= 3

x in <3:+oo)

x*(x-3)-4*abs(x-3/2) = 0

x in <0:3)

x*(-(x-3))-4*abs(x-3/2) = 0

-x*(-(x-3))-4*abs(x-3/2) = 0

x in (-oo:0)

abs(x-3/2)

x-3/2 >= 0

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

x >= 3/2

x in (-oo:0)

-x*(-(x-3))-4*(-(x-3/2)) = 0

x*(-(x-3))-4*abs(x-3/2) = 0

x in <0:3)

abs(x-3/2)

x-3/2 >= 0

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

x >= 3/2

x in <3/2:3)

x*(-(x-3))-4*(x-3/2) = 0

x in <0:3/2)

x*(-(x-3))-4*(-(x-3/2)) = 0

x*(x-3)-4*abs(x-3/2) = 0

x in <3:+oo)

abs(x-3/2)

x-3/2 >= 0

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

x >= 3/2

x in <3:+oo)

x*(x-3)-4*(x-3/2) = 0

abs(x)*abs(x-3)-4*abs(x-3/2) = 0


/
| -x*(-(x-3))-4*(-(x-3/2)) = 0 i x in (-oo:0)
| x*(-(x-3))-4*(-(x-3/2)) = 0 i x in <0:3/2)
| x*(-(x-3))-4*(x-3/2) = 0 i x in <3/2:3)
| x*(x-3)-4*(x-3/2) = 0 i x in <3:+oo)


x in (-oo:0)

-x*(-(x-3))-4*(-(x-3/2)) = 0

-x*(3-x)-4*(3/2-x) = 0

-x*(3-x)-4*(3/2-x) = 0

x^2+x-6 = 0

x^2+x-6 = 0

x^2+x-6 = 0

DELTA = 1^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(1*2) or x = (-25^(1/2)-1)/(1*2)

x = 2 or x = -3

(x+3)*(x-2) = 0

(x+3)*(x-2) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-2 )

x-2 = 0 // + 2

x = 2

x in <0:3/2)

x*(-(x-3))-4*(-(x-3/2)) = 0

x*(3-x)-4*(3/2-x) = 0

x*(3-x)-4*(3/2-x) = 0

7*x-x^2-6 = 0

7*x-x^2-6 = 0

7*x-x^2-6 = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)-7)/(-1*2) or x = (-25^(1/2)-7)/(-1*2)

x = 1 or x = 6

(x-1)*(x-6) = 0

(x-1)*(x-6) = 0

( x-1 )

x-1 = 0 // + 1

x = 1

( x-6 )

x-6 = 0 // + 6

x = 6

x in <3/2:3)

x*(-(x-3))-4*(x-3/2) = 0

x*(3-x)-4*(x-3/2) = 0

x*(3-x)-4*(x-3/2) = 0

6-x^2-x = 0

6-x^2-x = 0

6-x^2-x = 0

DELTA = (-1)^2-(-1*4*6)

DELTA = 25

DELTA > 0

x = (25^(1/2)+1)/(-1*2) or x = (1-25^(1/2))/(-1*2)

x = -3 or x = 2

(x+3)*(x-2) = 0

(x+3)*(x-2) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-2 )

x-2 = 0 // + 2

x = 2

x in <3:+oo)

x*(x-3)-4*(x-3/2) = 0

x*(x-3)-4*(x-3/2) = 0

x^2-7*x+6 = 0

x^2-7*x+6 = 0

x^2-7*x+6 = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)+7)/(1*2) or x = (7-25^(1/2))/(1*2)

x = 6 or x = 1

(x-1)*(x-6) = 0

(x-1)*(x-6) = 0

( x-1 )

x-1 = 0 // + 1

x = 1

( x-6 )

x-6 = 0 // + 6

x = 6

x in { -3, 1, 2, 6 }

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