What are the solutions to the equation x(x-2)^2=x(1-2x)^2 ?

The solutions to the equation x(x-2)^2=x(1-2x)^2 are x=0,x=-1,x=1

Find the zeros of x(x-2)^2=x(1-2x)^2

The zeros of x(x-2)^2=x(1-2x)^2 are x=0,x=-1,x=1

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x (x - 2)^{2} = x (1 - 2 x)^{2}

x = 0, x = - 1, x = 1

Solution steps

x (x - 2)^{2} = x (1 - 2 x)^{2}

Move

x (1 - 2 x)^{2}

to the left side

x (x - 2)^{2} - x (1 - 2 x)^{2} = 0

Factor

x (x - 2)^{2} - x (1 - 2 x)^{2} : - 3 x (x + 1) (x - 1)

- 3 x (x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 1 = 0 or x - 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = 0, x = - 1, x = 1

x^{3} = - 115

x^{8} + 48 x^{4} = 49

4 x^{3} + 6 x^{2} = 0

(z - 1)^{3} = 2

500 = 4 x^{3} - 80 x^{2} + 400 x

What are the solutions to the equation x(x-2)^2=x(1-2x)^2 ?
The solutions to the equation x(x-2)^2=x(1-2x)^2 are x=0,x=-1,x=1
Find the zeros of x(x-2)^2=x(1-2x)^2
The zeros of x(x-2)^2=x(1-2x)^2 are x=0,x=-1,x=1