What are the solutions to the equation x^3=3x^2 ?

The solutions to the equation x^3=3x^2 are x=0,x=3

Find the zeros of x^3=3x^2

The zeros of x^3=3x^2 are x=0,x=3

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x^{3} = 3 x^{2}

x = 0, x = 3

Solution steps

x^{3} = 3 x^{2}

Move

3 x^{2}

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 3 = 0

Solve

x - 3 = 0 : x = 3

The solutions are

x = 0, x = 3

2 x^{3} - 24 x^{2} + 64 x = 0

x^{3} + 4 x^{2} + 8 x + 10 = 0

x^{4} - 20 x^{2} + 99 = 0

3 x (8 x - 9) (x^{2} + 64) = 0

0 = x^{3} - x^{2} - 5 x + 5

What are the solutions to the equation x^3=3x^2 ?
The solutions to the equation x^3=3x^2 are x=0,x=3
Find the zeros of x^3=3x^2
The zeros of x^3=3x^2 are x=0,x=3