What are the solutions to the equation 6x^4-29x^3+30x^2=6-11x ?

The solutions to the equation 6x^4-29x^3+30x^2=6-11x are x=2,x=3,x= 1/3 ,x=-1/2

Find the zeros of 6x^4-29x^3+30x^2=6-11x

The zeros of 6x^4-29x^3+30x^2=6-11x are x=2,x=3,x= 1/3 ,x=-1/2

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6 x^{4} - 29 x^{3} + 30 x^{2} = 6 - 11 x

x = 2, x = 3, x = \frac{1}{3}, x = - \frac{1}{2}

Decimal Notation

x = 2, x = 3, x = 0.33333 \dots, x = - 0.5

Solution steps

6 x^{4} - 29 x^{3} + 30 x^{2} = 6 - 11 x

Move

11 x

to the left side

6 x^{4} - 29 x^{3} + 30 x^{2} + 11 x = 6

Move

6

to the left side

6 x^{4} - 29 x^{3} + 30 x^{2} + 11 x - 6 = 0

Factor

6 x^{4} - 29 x^{3} + 30 x^{2} + 11 x - 6 : (x - 2) (x - 3) (3 x - 1) (2 x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x - 3 = 0 or 3 x - 1 = 0 or 2 x + 1 = 0

Solve

x - 2 = 0 : x = 2

Solve

x - 3 = 0 : x = 3

Solve

3 x - 1 = 0 : x = \frac{1}{3}

Solve

2 x + 1 = 0 : x = - \frac{1}{2}

The solutions are

x = 2, x = 3, x = \frac{1}{3}, x = - \frac{1}{2}

z^{5} + 1 = 0

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

16 x^{6} - 24 x^{4} + 9 x^{2} - 1 = 0

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

2 x^{3} - x^{2} - 12 = 0

What are the solutions to the equation 6x^4-29x^3+30x^2=6-11x ?
The solutions to the equation 6x^4-29x^3+30x^2=6-11x are x=2,x=3,x= 1/3 ,x=-1/2
Find the zeros of 6x^4-29x^3+30x^2=6-11x
The zeros of 6x^4-29x^3+30x^2=6-11x are x=2,x=3,x= 1/3 ,x=-1/2