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

2 Answers
Apr 6, 2016

x=0 or x=2/3

Explanation:

6x^2 - 4x = 0

=>2x(3x-2)=0

=>2x=0 OR 3x-2=0

=>x=0 OR x=2/3

Alternately:

Case 1: x=0
Then, 6x^2 = 6xx0xx0 = 0
And, 4x=4xx0=0
Left side = right side =>Equation holds.

Case 2: x!=0
6x^2 = 4x

Divide both sides by x:
6x=4

Divide both sides by 6 and simplify:
x=4/6
=>x=2/3

Apr 6, 2016

Answer: x= 0 or 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 4x to both sides of the equation

6x^2 = 4x

6x^2 - 4x = 0

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

2*3*x *x- 2*2*x= 0
2x(3x-2) = 0
2x= 0 " " " and 3x-2= 0

Step 3: Then solve for x

2x= 0

(2x)/2 = 0/2

x= 0

or

3x-2= 0

3x-2 + 2 = 0+2

3x = 2

(3x)/3 = 2/3
x= 2/3