What are the solutions to the equation 0=12t^3-48t^2+48t ?

The solutions to the equation 0=12t^3-48t^2+48t are t=0,t=2

Find the zeros of 0=12t^3-48t^2+48t

The zeros of 0=12t^3-48t^2+48t are t=0,t=2

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0 = 12 t^{3} - 48 t^{2} + 48 t

t = 0, t = 2

Solution steps

0 = 12 t^{3} - 48 t^{2} + 48 t

Switch sides

12 t^{3} - 48 t^{2} + 48 t = 0

Factor

12 t^{3} - 48 t^{2} + 48 t : 12 t (t - 2)^{2}

12 t (t - 2)^{2} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

t = 0 or t - 2 = 0

Solve

t - 2 = 0 : t = 2

The solutions are

t = 0, t = 2

24 x^{3} - 3 = 0

x^{4} + 62 x^{2} + 128 x + 65 = 0

x^{3} - 11 x^{2} + 26 x - 16 = 0

x^{3} + 4 x^{2} - 5 x - 20 = 0

x^{3} - 3 x^{2} - 13 x + 15

What are the solutions to the equation 0=12t^3-48t^2+48t ?
The solutions to the equation 0=12t^3-48t^2+48t are t=0,t=2
Find the zeros of 0=12t^3-48t^2+48t
The zeros of 0=12t^3-48t^2+48t are t=0,t=2