What are the solutions to the equation 6(x^2-3)-2x(3x^2+7)=15-2x ?

The solutions to the equation 6(x^2-3)-2x(3x^2+7)=15-2x are x\approx-1.19216…

Find the zeros of 6(x^2-3)-2x(3x^2+7)=15-2x

The zeros of 6(x^2-3)-2x(3x^2+7)=15-2x are x\approx-1.19216…

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6 (x^{2} - 3) - 2 x (3 x^{2} + 7) = 15 - 2 x

x \approx - 1.19216 \dots

Solution steps

6 (x^{2} - 3) - 2 x (3 x^{2} + 7) = 15 - 2 x

Expand

6 (x^{2} - 3) - 2 x (3 x^{2} + 7) : 6 x^{2} - 18 - 6 x^{3} - 14 x

6 x^{2} - 18 - 6 x^{3} - 14 x = 15 - 2 x

Move

2 x

to the left side

6 x^{2} - 18 - 6 x^{3} - 12 x = 15

Move

15

to the left side

- 6 x^{3} + 6 x^{2} - 12 x - 33 = 0

Find one solution for

- 6 x^{3} + 6 x^{2} - 12 x - 33 = 0

using Newton-Raphson:

x \approx - 1.19216 \dots

Apply long division:

\frac{- 6 x ^{3} + 6 x ^{2} - 12 x - 33}{x + 1.19216 \dots} = - 6 x^{2} + 13.15301 \dots x - 27.68062 \dots

- 6 x^{2} + 13.15301 \dots x - 27.68062 \dots \approx 0

Find one solution for

- 6 x^{2} + 13.15301 \dots x - 27.68062 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.19216 \dots

2 m^{3} + 12 m^{2} + 10 m = 0

2.5 x^{3} + 1.5 6^{2} - 3 x + 1.5 = 0

\frac{2 p ^{3}}{2} = 54

(y^{2} - y - 30) (5 y - 40) = 0

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

What are the solutions to the equation 6(x^2-3)-2x(3x^2+7)=15-2x ?
The solutions to the equation 6(x^2-3)-2x(3x^2+7)=15-2x are x\approx-1.19216…
Find the zeros of 6(x^2-3)-2x(3x^2+7)=15-2x
The zeros of 6(x^2-3)-2x(3x^2+7)=15-2x are x\approx-1.19216…