Question

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

Answer 1

Hint: We are given an equation and we have to find its factor. For this we can begin by setting the equation equal to zero. Then we will take the factor out of the common terms from the equation. First we will factor out the common variable from it then the digit. Then equate both the terms equal to zero and find the two values of x.

Complete step-by-step solution:
Step1: we are given an equation $6{x^2} = 4x$ first we will set the equation equal to zero.
$ \Rightarrow 6{x^2} = 4x$
$ \Rightarrow 6{x^2} - 4x = 0$
Then we will factor out the terms step by step from it. First we will factor out $x$ from it. We will get:
$ \Rightarrow x\left( {6x - 4} \right) = 0$
Now we will factor out the common term 2 from it:
$ \Rightarrow 2x\left( {3x - 2} \right) = 0$
Step2: Now we will equate both the terms equal to zero we will get:
$ \Rightarrow 2x = 0$
So, $x = 0$
Equating $\left( {3x - 2} \right)$ equal to zero we will get:
$ \Rightarrow 3x - 2 = 0$
$3x = 2$
Solving for $x$ we will get:
$x = \dfrac{2}{3}$

Hence the value of x is $0$ or $\dfrac{2}{3}$

Note: The main approach to solve these questions is to factor out the common terms correctly if then any identity can be applied so apply it or equate the terms equal to zero and solve for x.
Alternate method:
We will take two case
Case1: if $x = 0$. So we substitute the value of $x$ and get:
$6{x^2} = 6 \times 0 \times 0 = 0$
$4x = 4 \times 0 = 0$
L.H.S=R.H.S
Equation holds
Case2: $x \ne 0$
$6{x^2} = 4x$
Dividing both the sides by $x$ we will get:
$ \Rightarrow 6x = 4$
Dividing both sides by 6 we will get:
$ \Rightarrow x = \dfrac{2}{3}$
Hence $x = 0;\dfrac{2}{3}$