Factor completely.6, x, squared, minus, 19, x, plus, 146x 2 −19x+14

The expression you provided seems to have a typo. I believe you meant "6x^2 - 19x + 14". Here's how to factor it:

1. First, identify the coefficients in the quadratic equation. In this case, a = 6, b = -19, and c = 14.

2. Look for two numbers that multiply to give ac (which is 6*14 = 84) and add up to give b (which is -19).

3. The numbers that satisfy these conditions are -4 and -21 because -4*-21 = 84 and -4 + (-21) = -19.

4. Rewrite the middle term of the quadratic equation as the sum of the terms -4x and -21x. This gives us: 6x^2 - 4x - 15x + 14.

5. Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us: 2x(3x - 2) - 7(3x - 2).

6. Notice that (3x - 2) is a common factor. Factor out this term to get: (3x - 2)(2x - 7).

So, the factored form of the equation 6x^2 - 19x + 14 is (3x - 2)(2x - 7).

The expression you provided seems to have a typo. I believe you meant "6x^2 - 19x + 14". Let's factor this quadratic equation.

Step 1: Identify a, b, and c in the quadratic equation ax^2 + bx + c. Here, a = 6, b = -19, and c = 14.

Step 2: Find two numbers that multiply to give ac (a times c), and add to give b. So we need two numbers that multiply to 84 (6*14) and add to -19. These numbers are -4 and -21.

Step 3: Rewrite the equation, breaking up the middle term using the two numbers we found. We get: 6x^2 - 4x - 15x + 14.

Step 4: Factor by grouping. The first two terms share a common factor of 2x, and the last two terms share a common factor of -1:

2x(3x - 2) - 1(3x - 2)

Step 5: Notice that (3x - 2) is a common factor. So we can write the expression as:

(2x - 1)(3x - 2)

So, 6x^2 - 19x + 14 factors to (2x - 1)(3x - 2).