What are the solutions to the equation 4x^4+10x^3=6x^2+15x ?

The solutions to the equation 4x^4+10x^3=6x^2+15x are x=0,x=-5/2 ,x=-sqrt(3/2),x=sqrt(3/2)

Find the zeros of 4x^4+10x^3=6x^2+15x

The zeros of 4x^4+10x^3=6x^2+15x are x=0,x=-5/2 ,x=-sqrt(3/2),x=sqrt(3/2)

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4 x^{4} + 10 x^{3} = 6 x^{2} + 15 x

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

Decimal Notation

x = 0, x = - 2.5, x = - 1.22474 \dots, x = 1.22474 \dots

Solution steps

4 x^{4} + 10 x^{3} = 6 x^{2} + 15 x

Move

15 x

to the left side

4 x^{4} + 10 x^{3} - 15 x = 6 x^{2}

Move

6 x^{2}

to the left side

4 x^{4} + 10 x^{3} - 15 x - 6 x^{2} = 0

Factor

4 x^{4} + 10 x^{3} - 15 x - 6 x^{2} : x (2 x + 5) (2 x + 3) (2 x - 3)

x (2 x + 5) (2 x + 3) (2 x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

2 x + 3 = 0 : x = - \frac{3}{2}

Solve

2 x - 3 = 0 : x = \frac{3}{2}

The solutions are

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

r^{3} = 216

- x^{3} + 7 x + 6 = 0

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

- 2 x (3 x + 1) (x - 8) (x + 2) = 0

9 x^{4} + 27 x^{3} - 4 x^{2} - 12 x = 0

What are the solutions to the equation 4x^4+10x^3=6x^2+15x ?
The solutions to the equation 4x^4+10x^3=6x^2+15x are x=0,x=-5/2 ,x=-sqrt(3/2),x=sqrt(3/2)
Find the zeros of 4x^4+10x^3=6x^2+15x
The zeros of 4x^4+10x^3=6x^2+15x are x=0,x=-5/2 ,x=-sqrt(3/2),x=sqrt(3/2)