What are the solutions to the equation x^3-6x=3x^2-8 ?

The solutions to the equation x^3-6x=3x^2-8 are x=1,x=-2,x=4

Find the zeros of x^3-6x=3x^2-8

The zeros of x^3-6x=3x^2-8 are x=1,x=-2,x=4

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x^{3} - 6 x = 3 x^{2} - 8

x = 1, x = - 2, x = 4

Solution steps

x^{3} - 6 x = 3 x^{2} - 8

Move

8

to the left side

x^{3} - 6 x + 8 = 3 x^{2}

Move

3 x^{2}

to the left side

x^{3} - 6 x + 8 - 3 x^{2} = 0

Write in the standard form

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

x^{3} - 3 x^{2} - 6 x + 8 = 0

Factor

x^{3} - 3 x^{2} - 6 x + 8 : (x - 1) (x + 2) (x - 4)

(x - 1) (x + 2) (x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 2 = 0 or x - 4 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 2 = 0 : x = - 2

Solve

x - 4 = 0 : x = 4

The solutions are

x = 1, x = - 2, x = 4

y^{4} - 4 y = 0

3 s^{3} - 5 s + 2 = 0

4 x^{4} + 5 x^{2} - 9 = 0

(x^{2} + 4 x)^{2} - 17 (x^{2} + 4 x) = 60

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

What are the solutions to the equation x^3-6x=3x^2-8 ?
The solutions to the equation x^3-6x=3x^2-8 are x=1,x=-2,x=4
Find the zeros of x^3-6x=3x^2-8
The zeros of x^3-6x=3x^2-8 are x=1,x=-2,x=4