# how to solve by factorization and can you explain? x^2= 6x

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to move all terms that contain x to one side such that:

`x^2 - 6x = 0 `

Notice that both terms have a common factor x, hence, factoring out x yields:

`x(x - 6) = 0`

Since a product of two factors is 0 when a factor or both are zeroes, hence,  you need to set the following equations such that:

`{(x=0),(x-6=0):} =gt {(x=0),(x=6):}`

Hence, evaluating the solution to the given equation using factorization, yields `x = 0`  and `x = 6.` `.`

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The equation x^2= 6x has to be solved.

x^2 = 6x

Subtract 6x from both the sides

x^2 - 6x = 6x - 6x

x^2 - 6x = 0

Isolate the common factor x.

x(x - 6) = 0

x - 6 = 0 gives x = 6

The solution of the equation x^2 = 6x  is x = 0 and x = 6

widowspeak | (Level 1) Honors

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In order to solve bu factorization, you want to get each equation in a form where the right-hand side equals zero. So for the first case: x^2 = 6x is equivalent to x^2 - 6x =0.
We then try to factorize the left-hand side. Both terms involve x so we can factorize that out: x^2 - 6x = x*(x - 6)

Hence x*(x-6) = 0. Now, because we get zero whenever we multiply something by zero, the equation implies that either x=0 or x-6=0. Hence x=0 or 6.

For the second equation: 2x^2 = x/3 => 2x^2 - x/3 = 0 => 6x^2 - x =0.

As before we can see that x is a common factor so we get

6x^2 - x = x*(6x - 1)

So either x =0 or 6x - 1 =0 => 6x=1 => x=1/6. So x= 0 or 1/6.

For the third equation: x/5 - x^2 = 0 => x - 5*x^2 = 0 => x*(1 - 5x) = 0 => Either x=0 or 1-5x=0

For 1 - 5*x = 0 => 5*x = 1 => x = 1/5

hence either x=0 or x=1/5.