What are the solutions to the equation 15t^3-15t^2+20t=5t ?

The solutions to the equation 15t^3-15t^2+20t=5t are t=0,t= 1/2+i(sqrt(3))/2 ,t= 1/2-i(sqrt(3))/2

Find the zeros of 15t^3-15t^2+20t=5t

The zeros of 15t^3-15t^2+20t=5t are t=0,t= 1/2+i(sqrt(3))/2 ,t= 1/2-i(sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

15 t^{3} - 15 t^{2} + 20 t = 5 t

t = 0, t = \frac{1}{2} + i \frac{3}{2}, t = \frac{1}{2} - i \frac{3}{2}

Solution steps

15 t^{3} - 15 t^{2} + 20 t = 5 t

Move

5 t

to the left side

15 t^{3} - 15 t^{2} + 15 t = 0

Factor

15 t^{3} - 15 t^{2} + 15 t : 15 t (t^{2} - t + 1)

15 t (t^{2} - t + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

t = 0 or t^{2} - t + 1 = 0

Solve

t^{2} - t + 1 = 0 : t = \frac{1}{2} + i \frac{3}{2}, t = \frac{1}{2} - i \frac{3}{2}

The solutions are

t = 0, t = \frac{1}{2} + i \frac{3}{2}, t = \frac{1}{2} - i \frac{3}{2}

x, x^{3} + y^{3} = 16

x^{3} = \frac{27}{125}

(x - 3)^{3} = 8

x^{3} - 12 x^{2} + 36 x = 0

x^{3} - x^{2} - 30 x = 0

What are the solutions to the equation 15t^3-15t^2+20t=5t ?
The solutions to the equation 15t^3-15t^2+20t=5t are t=0,t= 1/2+i(sqrt(3))/2 ,t= 1/2-i(sqrt(3))/2
Find the zeros of 15t^3-15t^2+20t=5t
The zeros of 15t^3-15t^2+20t=5t are t=0,t= 1/2+i(sqrt(3))/2 ,t= 1/2-i(sqrt(3))/2