What are the solutions to the equation 12x-6x^2+3x^4=6x^3+2x-x^4 ?

The solutions to the equation 12x-6x^2+3x^4=6x^3+2x-x^4 are x=0,x\approx-1.26116…

Find the zeros of 12x-6x^2+3x^4=6x^3+2x-x^4

The zeros of 12x-6x^2+3x^4=6x^3+2x-x^4 are x=0,x\approx-1.26116…

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12 x - 6 x^{2} + 3 x^{4} = 6 x^{3} + 2 x - x^{4}

x = 0, x \approx - 1.26116 \dots

Solution steps

12 x - 6 x^{2} + 3 x^{4} = 6 x^{3} + 2 x - x^{4}

Subtract

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

from both sides

12 x - 6 x^{2} + 3 x^{4} - (6 x^{3} + 2 x - x^{4}) = 6 x^{3} + 2 x - x^{4} - (6 x^{3} + 2 x - x^{4})

Simplify

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 x^{3} - 3 x^{2} - 3 x + 5 = 0

Solve

2 x^{3} - 3 x^{2} - 3 x + 5 = 0 : x \approx - 1.26116 \dots

The solutions are

x = 0, x \approx - 1.26116 \dots

4 x^{3} + 56 x^{2} + 132 x = 0

125 t^{10} - 3 t^{7} = 0

- 3 x^{3} + 40 x^{2} - 90 x + 150 = 0

x^{3} - 11 x^{2} - 16 x + 176 = 0

y, x = y^{5}

What are the solutions to the equation 12x-6x^2+3x^4=6x^3+2x-x^4 ?
The solutions to the equation 12x-6x^2+3x^4=6x^3+2x-x^4 are x=0,x\approx-1.26116…
Find the zeros of 12x-6x^2+3x^4=6x^3+2x-x^4
The zeros of 12x-6x^2+3x^4=6x^3+2x-x^4 are x=0,x\approx-1.26116…