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

The solutions to the equation 3x(x-2)=6x^2-8x are x=0,x= 2/3

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

The zeros of 3x(x-2)=6x^2-8x are x=0,x= 2/3

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

x = 0, x = \frac{2}{3}

Decimal Notation

x = 0, x = 0.66666 \dots

Solution steps

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

Expand

3 x (x - 2) : 3 x^{2} - 6 x

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

Move

8 x

to the left side

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

Move

6 x^{2}

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 ( - 3 ) \cdot 0}{2 ( - 3 )}

2^{2} - 4 (- 3) \cdot 0 = 2

x_{1, 2} = \frac{- 2 \pm 2}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- 2 + 2}{2 ( - 3 )}, x_{2} = \frac{- 2 - 2}{2 ( - 3 )}

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

x = \frac{- 2 - 2}{2 ( - 3 )} : \frac{2}{3}

The solutions to the quadratic equation are:

x = 0, x = \frac{2}{3}

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

5 x^{2} + 7 x = 5

11 + w^{2} = 2

x, x y - x^{2} = 4 y + x

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

What are the solutions to the equation 3x(x-2)=6x^2-8x ?
The solutions to the equation 3x(x-2)=6x^2-8x are x=0,x= 2/3
Find the zeros of 3x(x-2)=6x^2-8x
The zeros of 3x(x-2)=6x^2-8x are x=0,x= 2/3