What are the solutions to the equation z^3-z^2-12z=0 ?

The solutions to the equation z^3-z^2-12z=0 are z=0,z=-3,z=4

Find the zeros of z^3-z^2-12z=0

The zeros of z^3-z^2-12z=0 are z=0,z=-3,z=4

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z^{3} - z^{2} - 12 z = 0

z = 0, z = - 3, z = 4

Solution steps

z^{3} - z^{2} - 12 z = 0

Factor

z^{3} - z^{2} - 12 z : z (z + 3) (z - 4)

z (z + 3) (z - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

z = 0 or z + 3 = 0 or z - 4 = 0

Solve

z + 3 = 0 : z = - 3

Solve

z - 4 = 0 : z = 4

The solutions are

z = 0, z = - 3, z = 4

4 x^{3} - 24 x^{2} - 60 x = 0

(z - 2)^{3} = - 64

x, 2 x^{3} + 10 x^{2} - 24 = 0

4 x^{3} + 2 x - 18 = 0

y, x^{3} + y^{3} = 8

What are the solutions to the equation z^3-z^2-12z=0 ?
The solutions to the equation z^3-z^2-12z=0 are z=0,z=-3,z=4
Find the zeros of z^3-z^2-12z=0
The zeros of z^3-z^2-12z=0 are z=0,z=-3,z=4