How do you solve  6x^2=4x ?

Apr 6, 2016

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

Explanation:

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

$\implies 2 x \left(3 x - 2\right) = 0$

$\implies 2 x = 0$ OR $3 x - 2 = 0$

$\implies x = 0$ OR $x = \frac{2}{3}$

Alternately:

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

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

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

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

Apr 6, 2016

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

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 $4 x$ to both sides of the equation

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

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

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

$2 \cdot 3 \cdot x \cdot x - 2 \cdot 2 \cdot x = 0$
$2 x \left(3 x - 2\right) = 0$
$2 x = 0$ $\text{ " } \mathmr{and}$ $3 x - 2 = 0$

Step 3: Then solve for $x$

$2 x = 0$

$\frac{2 x}{2} = \frac{0}{2}$

$x = 0$

or

$3 x - 2 = 0$

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

$3 x = 2$

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