What are the solutions to the equation 3x-1=3x^3-x^2 ?

The solutions to the equation 3x-1=3x^3-x^2 are x= 1/3 ,x=-1,x=1

Find the zeros of 3x-1=3x^3-x^2

The zeros of 3x-1=3x^3-x^2 are x= 1/3 ,x=-1,x=1

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3 x - 1 = 3 x^{3} - x^{2}

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

Decimal Notation

x = 0.33333 \dots, x = - 1, x = 1

Solution steps

3 x - 1 = 3 x^{3} - x^{2}

Switch sides

3 x^{3} - x^{2} = 3 x - 1

Move

1

to the left side

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

Move

3 x

to the left side

3 x^{3} - x^{2} + 1 - 3 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

3 x^{3} - x^{2} - 3 x + 1 = 0

Factor

3 x^{3} - x^{2} - 3 x + 1 : (3 x - 1) (x + 1) (x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

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

c^{3} = 49

x^{3} + a = c

8 y^{3} - 216 = 0

x^{4} - 36 x^{2} + 35 = 0

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

What are the solutions to the equation 3x-1=3x^3-x^2 ?
The solutions to the equation 3x-1=3x^3-x^2 are x= 1/3 ,x=-1,x=1
Find the zeros of 3x-1=3x^3-x^2
The zeros of 3x-1=3x^3-x^2 are x= 1/3 ,x=-1,x=1