SOLUTION: How would you solve this equation? x(x+1/3)(2x-3)=0

Question 124826: How would you solve this equation?
x(x+1/3)(2x-3)=0
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The easiest way to solve this equation is to notice that the left side is the product of
three factors. Since the right side of the equation is zero, the equation will be true if
one of the factors on the left side is zero, because multiplying the three factors together when
one of the factors is zero makes the entire left side become zero and therefore the left side
equals the right side.
.
The first factor is x. Set it equal to zero and you have one of the values for x that will make
the entire left side equal to zero. That value is x = 0.
.
Next set the second factor equal to zero and solve for the value of x that makes that factor
equal to zero. The second factor is (x + 1/3) and setting it equal to zero results in:
.
x + 1/3 = 0
.
Get rid of the +1/3 on the left side by subtracting 1/3 from both sides and you have:
.
x = -1/3
.
That is the second value of x that will make the equation true ... that is will make the left
side equal to zero and therefore equal to the right side.
.
Finally, the third factor is (2x - 3). Set it equal to zero and you get:
.
2x - 3 = 0
.
Get rid of the -3 on the left side by adding +3 to both sides. When you do that addition
the -3 and the +3 cancel on the left side and the equation that results is:
.
2x = +3
.
Solve for x by dividing both sides by 2 and you get:
.
x = 3/2
.
You now have found all three values of x that will satisfy this equation. Those values are:
.
x = 0
x = -1/3 and
x = 3/2
.
If you wanted to prove this to yourself, you could multiply the three factors out on the
left side ... then one at a time you could substitute the three values into the multiplied
out equation and you would find that each of these three values would make the multiplied
out left side become zero and therefore equal to the zero on the right side.
.
Hope this helps you to see the easy way to solve this equation.
.

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