What are the solutions to the equation 2x(x-2)^3+3x^2(x-2)^2=0 ?

The solutions to the equation 2x(x-2)^3+3x^2(x-2)^2=0 are x=0,x=2,x= 4/5

Find the zeros of 2x(x-2)^3+3x^2(x-2)^2=0

The zeros of 2x(x-2)^3+3x^2(x-2)^2=0 are x=0,x=2,x= 4/5

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2 x (x - 2)^{3} + 3 x^{2} (x - 2)^{2} = 0

x = 0, x = 2, x = \frac{4}{5}

Decimal Notation

x = 0, x = 2, x = 0.8

Solution steps

2 x (x - 2)^{3} + 3 x^{2} (x - 2)^{2} = 0

Factor

2 x (x - 2)^{3} + 3 x^{2} (x - 2)^{2} : x (x - 2)^{2} (5 x - 4)

x (x - 2)^{2} (5 x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 2 = 0 or 5 x - 4 = 0

Solve

x - 2 = 0 : x = 2

Solve

5 x - 4 = 0 : x = \frac{4}{5}

The solutions are

x = 0, x = 2, x = \frac{4}{5}

0 = 4 x^{3} - 12 x^{2}

x^{9} + x^{6} - 36 = 0

- 4500 x^{3} - 1950 x^{2} - 205 x - 3 = 0

(x^{2} + 2 x)^{2} - 2 (x^{2} + 2 x) - 3 = 0

x, 9 x^{6} - 7 x^{2} = 0

What are the solutions to the equation 2x(x-2)^3+3x^2(x-2)^2=0 ?
The solutions to the equation 2x(x-2)^3+3x^2(x-2)^2=0 are x=0,x=2,x= 4/5
Find the zeros of 2x(x-2)^3+3x^2(x-2)^2=0
The zeros of 2x(x-2)^3+3x^2(x-2)^2=0 are x=0,x=2,x= 4/5