(2x+1)(3x-1)=0
can u please show me the steps to solve this problem thanks
The first impulse would be to multiply those quantities, but that would be
a waste of time, because you would then need to factor the result. You already
have the factors staring you in the face.
What the problem is telling you is that one, or both, of those factors has to
be equal to zero. Remember, multiplying by zero gives a zero result. So, we
set each quantity to zero and solve for x.
2x + 1 = 0
2x = -1
x = -1/2
3x - 1 = 0
3x = 1
x = 1/3
Now, if you want to, you can multiply the factors and use the resulting
equation to check your answers.
(2x + 1)(3x - 1) = 0
6x^2 + 3x - 2x - 1 = 0
6x^2 + x - 1 = 0
Plug in the values calculated for x.
6x^2 + x - 1 = 0
6(-1/2)^2 + (-1/2) - 1 = 0
6(1/4) - 1/2 - 1 = 0
1 1/2 - 1/2 - 1 = 0
0 = 0
That one checks.
6x^2 + x - 1 = 0
6(1/3)^2 + 1/3 - 1 = 0
6(1/9) + 1/3 - 1 = 0
2/3 + 1/3 - 1 = 0
0 = 0
That one checks, too.
x = -1/2 and x = 1/3