What are the solutions to the equation (x^2+x)(x+6-x^3)=5x ?

The solutions to the equation (x^2+x)(x+6-x^3)=5x are x=0,x\approx-0.14629…,x\approx 1.82220…

Find the zeros of (x^2+x)(x+6-x^3)=5x

The zeros of (x^2+x)(x+6-x^3)=5x are x=0,x\approx-0.14629…,x\approx 1.82220…

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(x^{2} + x) (x + 6 - x^{3}) = 5 x

x = 0, x \approx - 0.14629 \dots, x \approx 1.82220 \dots

Solution steps

(x^{2} + x) (x + 6 - x^{3}) = 5 x

Move

5 x

to the left side

(x^{2} + x) (x + 6 - x^{3}) - 5 x = 0

Factor

(x^{2} + x) (x + 6 - x^{3}) - 5 x : - x (x^{4} + x^{3} - x^{2} - 7 x - 1)

- x (x^{4} + x^{3} - x^{2} - 7 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{4} + x^{3} - x^{2} - 7 x - 1 = 0

Solve

x^{4} + x^{3} - x^{2} - 7 x - 1 = 0 : x \approx - 0.14629 \dots, x \approx 1.82220 \dots

The solutions are

x = 0, x \approx - 0.14629 \dots, x \approx 1.82220 \dots

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

x^{3} - x = 4

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

(z + 2)^{3} = z^{2} + 5 z + 2

m^{3} - 10 m + 1 = 0

What are the solutions to the equation (x^2+x)(x+6-x^3)=5x ?
The solutions to the equation (x^2+x)(x+6-x^3)=5x are x=0,x\approx-0.14629…,x\approx 1.82220…
Find the zeros of (x^2+x)(x+6-x^3)=5x
The zeros of (x^2+x)(x+6-x^3)=5x are x=0,x\approx-0.14629…,x\approx 1.82220…