How do you solve $6 x^{2} = 4 x$ $6x^2=4x$ ?

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How do you solve $6 x^{2} = 4 x$ $6x^2=4x$ ?

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Answer 1 · 2016-04-06T05:19:34

$x = 0$ $x=0$ or $x = \frac{2}{3}$ $x=2/3$

Explanation:

$6 x^{2} - 4 x = 0$ $6x^2 - 4x = 0$

$\Rightarrow 2 x (3 x - 2) = 0$ $=>2x(3x-2)=0$

$\Rightarrow 2 x = 0$ $=>2x=0$ OR $3 x - 2 = 0$ $3x-2=0$

$\Rightarrow x = 0$ $=>x=0$ OR $x = \frac{2}{3}$ $x=2/3$

Alternately:

Case 1: $x = 0$ $x=0$
Then, $6 x^{2} = 6 \times 0 \times 0 = 0$ $6x^2 = 6xx0xx0 = 0$
And, $4 x = 4 \times 0 = 0$ $4x=4xx0=0$
Left side = right side $\Rightarrow$ $=>$ Equation holds.

Case 2: $x \neq 0$ $x!=0$
$6 x^{2} = 4 x$ $6x^2 = 4x$

Divide both sides by $x$ $x$ :
$6 x = 4$ $6x=4$

Divide both sides by 6 and simplify:
$x = \frac{4}{6}$ $x=4/6$
$\Rightarrow x = \frac{2}{3}$ $=>x=2/3$

Answer 2 · 2016-04-06T05:23:19

Answer: $x = 0$ $x= 0$ or $x = \frac{2}{3}$ $x= 2/3$

Explanation:

Note: This equation is that of a 2nd degree polynomial or quadratic equation. To solve quadratic equation we must set it equation to zero first.

Step 1: Set the equation equal to zero by subtract $4 x$ $4x$ to both sides of the equation

$6 x^{2} = 4 x$ $6x^2 = 4x$

$6 x^{2} - 4 x = 0$ $6x^2 - 4x = 0$

Step 2: Factor out the greatest common factor of GCF like this

$2 \cdot 3 \cdot x \cdot x - 2 \cdot 2 \cdot x = 0$ $2*3*x *x- 2*2*x= 0$
$2 x (3 x - 2) = 0$ $2x(3x-2) = 0$
$2 x = 0$ $2x= 0$ $and$ $" " " and$ $3 x - 2 = 0$ $3x-2= 0$

Step 3: Then solve for $x$ $x$

$2 x = 0$ $2x= 0$

$\frac{2 x}{2} = \frac{0}{2}$ $(2x)/2 = 0/2$

$x = 0$ $x= 0$

or

$3 x - 2 = 0$ $3x-2= 0$

$3 x - 2 + 2 = 0 + 2$ $3x-2 + 2 = 0+2$

$3 x = 2$ $3x = 2$

$\frac{3 x}{3} = \frac{2}{3}$ $(3x)/3 = 2/3$
$x = \frac{2}{3}$ $x= 2/3$

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How do you solve $6 x^{2} = 4 x$ $6x^2=4x$ ?

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