6x^2=32x+24 Need help learning factoring please put work so I can understand

2 • (x - 6) • (3x + 2)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

STEP 1 : Equation at the end of step 1

((2•3x2) - 32x) - 24

STEP 2 : Pulling out like terms

Pull out like factors :

6x2 - 32x - 24 = 2 • (3x2 - 16x - 12)

Trying to factor by splitting the middle term

Factoring 3x2 - 16x - 12

The first term is, 3x2 its coefficient is 3 .

The middle term is, -16x its coefficient is -16 .

The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 3 • -12 = -36

Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -16 .

-36 + 1 = -35

-18 + 2 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -18 and 2

3x2 - 18x + 2x - 12

Step-4 : Add up the first 2 terms, pulling out like factors :

3x • (x-6)

Add up the last 2 terms, pulling out common factors :

2 • (x-6)

Step-5 : Add up the four terms of step 4 :

(3x+2) • (x-6)

Which is the desired factorization

Final result : 2 • (x - 6) • (3x + 2)

Hope this helps~

Smoll mochi

your answer would be 12

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!