What are the solutions to the equation x x/2 x/3 2=2x ?

The solutions to the equation x x/2 x/3 2=2x are x=0,x=-sqrt(6),x=sqrt(6)

Find the zeros of x x/2 x/3 2=2x

The zeros of x x/2 x/3 2=2x are x=0,x=-sqrt(6),x=sqrt(6)

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x \frac{x}{2} \frac{x}{3} 2 = 2 x

x = 0, x = - 6, x = 6

Decimal Notation

x = 0, x = - 2.44948 \dots, x = 2.44948 \dots

Solution steps

x \frac{x}{2} \cdot \frac{x}{3} \cdot 2 = 2 x

Move

2 x

to the left side

\frac{x ^{3}}{3} - 2 x = 0

Factor

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

x (\frac{1}{3} x + 2) (\frac{1}{3} x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or \frac{1}{3} x + 2 = 0 or \frac{1}{3} x - 2 = 0

Solve

\frac{1}{3} x + 2 = 0 : x = - 6

Solve

\frac{1}{3} x - 2 = 0 : x = 6

The solutions are

x = 0, x = - 6, x = 6

6 q^{3} + 6 = 2 q^{3} + 506

(x - 1)^{5} = x^{2} (x - 3) + x

x^{5} - x - 2 = 0

x^{6} - 26 x^{3} = 27

2 x^{4} + 3 x^{3} + 5 x^{2} + 2 x + 6 = 0

What are the solutions to the equation x x/2 x/3 2=2x ?
The solutions to the equation x x/2 x/3 2=2x are x=0,x=-sqrt(6),x=sqrt(6)
Find the zeros of x x/2 x/3 2=2x
The zeros of x x/2 x/3 2=2x are x=0,x=-sqrt(6),x=sqrt(6)