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

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Answer 1 · 2016-04-06T05:19:34

#x=0# or #x=2/3#

#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#

Answer 2 · 2016-04-06T05:23:19

Answer: #x= 0 # or #x= 2/3#

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#