how do you unfoil 3xsquared+5x-2=0?

Rearrange equation into:

3x²-x + 6x-2
=x(3x-1) + 2(3x-1)
=(x+2)(3x-1)

or use the quadratic formula,
or by completing squares.

how did you get the 6x?

5x = -x + 6x

To unfoil the equation 3x^2 + 5x - 2 = 0, we need to solve for the value(s) of x that make the equation true. This process is known as factoring or factoring by grouping. Here's how you can do it step by step:

Step 1: Look for two numbers that multiply to give the product of the coefficient of the x^2 term (3) and the constant term (-2), which is -6.

The possible number combinations are:
-6 x 1
-3 x 2
-2 x 3
-1 x 6

Step 2: Find the pair of numbers that also adds up to the coefficient of the x term (+5 in this case). The numbers -1 and 6 satisfy this condition.

Step 3: Split the middle term (+5x) of the original equation using the pair of numbers found in Step 2. We get:

3x^2 - 1x + 6x - 2 = 0

Step 4: Group the terms in pairs:

(3x^2 - 1x) + (6x - 2) = 0

Step 5: Factor out the greatest common factor (GCF) from each group:

x(3x - 1) + 2(3x - 1) = 0

Step 6: Notice that both groups now have a common factor, (3x - 1). Factor it out:

(3x - 1)(x + 2) = 0

Step 7: Apply the zero-product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero. Set each factor equal to zero and solve for x.

3x - 1 = 0 or x + 2 = 0

Solving these equations gives us the values of x:

3x = 1 --> x = 1/3
x = -2

So, the solutions to the equation 3x^2 + 5x - 2 = 0 are x = 1/3 and x = -2.