solve for x
3x^2-18x=0
Start by factoring out 3x.
3x(x - 6) = 0
So, 3x = 0 or (x-6) = 0
3x = 0
x = 0
(x - 6) = 0
x = 6
x = 0,6
To solve for x in the equation 3x^2 - 18x = 0, we can set the equation equal to zero and then factor it. This will help us find the values of x that satisfy the equation.
Step 1: Set the equation equal to zero:
3x^2 - 18x = 0
Step 2: Factor out the greatest common factor, if possible:
In this case, both terms have a common factor of 3x. By factoring that out, we get:
3x(x - 6) = 0
Step 3: Apply the zero product property:
When the product of two factors equals zero, at least one of the factors must also be zero. Since we have 3x and (x - 6) as factors, we can set each factor equal to zero and solve for x separately.
Setting 3x = 0:
3x = 0
Divide both sides by 3:
x = 0
Setting (x - 6) = 0:
x - 6 = 0
Add 6 to both sides:
x = 6
Step 4: Check for extraneous solutions:
To ensure that these solutions are valid, substitute the values of x back into the original equation. If both solutions satisfy the equation, then they are valid.
For x = 0:
3(0)^2 - 18(0) = 0
0 - 0 = 0
0 = 0 (True)
For x = 6:
3(6)^2 - 18(6) = 0
108 - 108 = 0
0 = 0 (True)
So, the solutions to the equation 3x^2 - 18x = 0 are x = 0 and x = 6.