What are the solutions to the equation 15x^5-20x^4=6x^3-8x^2 ?

The solutions to the equation 15x^5-20x^4=6x^3-8x^2 are x=0,x= 4/3 ,x=-sqrt(2/5),x=sqrt(2/5)

Find the zeros of 15x^5-20x^4=6x^3-8x^2

The zeros of 15x^5-20x^4=6x^3-8x^2 are x=0,x= 4/3 ,x=-sqrt(2/5),x=sqrt(2/5)

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15 x^{5} - 20 x^{4} = 6 x^{3} - 8 x^{2}

x = 0, x = \frac{4}{3}, x = - \frac{2}{5}, x = \frac{2}{5}

Decimal Notation

x = 0, x = 1.33333 \dots, x = - 0.63245 \dots, x = 0.63245 \dots

Solution steps

15 x^{5} - 20 x^{4} = 6 x^{3} - 8 x^{2}

Move

8 x^{2}

to the left side

15 x^{5} - 20 x^{4} + 8 x^{2} = 6 x^{3}

Move

6 x^{3}

to the left side

15 x^{5} - 20 x^{4} + 8 x^{2} - 6 x^{3} = 0

Factor

15 x^{5} - 20 x^{4} + 8 x^{2} - 6 x^{3} : x^{2} (3 x - 4) (5 x + 2) (5 x - 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x - 4 = 0 or 5 x + 2 = 0 or 5 x - 2 = 0

Solve

3 x - 4 = 0 : x = \frac{4}{3}

Solve

5 x + 2 = 0 : x = - \frac{2}{5}

Solve

5 x - 2 = 0 : x = \frac{2}{5}

The solutions are

x = 0, x = \frac{4}{3}, x = - \frac{2}{5}, x = \frac{2}{5}

5 x^{4} + 12 = x - 12

v^{2} + v^{3} = 12

x^{3} - 11 x^{2} + 18 x = 0

x^{4} + 1 = 2 x^{2}

x^{3} - 2 x^{2} - 4 x - 8 = 0

What are the solutions to the equation 15x^5-20x^4=6x^3-8x^2 ?
The solutions to the equation 15x^5-20x^4=6x^3-8x^2 are x=0,x= 4/3 ,x=-sqrt(2/5),x=sqrt(2/5)
Find the zeros of 15x^5-20x^4=6x^3-8x^2
The zeros of 15x^5-20x^4=6x^3-8x^2 are x=0,x= 4/3 ,x=-sqrt(2/5),x=sqrt(2/5)