24x^4-12x^3+48x^2/-4x=6x^3-3x^2-4x

If you want to check your answer, just multiply -4x(6x^3-3x^2-4x). You will find out that you need to check your signs and your division.

24x^4-12x^3+48x^2/-4x

this problem is divide by negative 4x
so my answer is should be 6x^3+3x^2+12x^
let me know if this right.

It should be -6x^3+3x^2-12x. You just had a few signs wrong.

To solve the equation:

24x^4 - 12x^3 + 48x^2 / -4x = 6x^3 - 3x^2 - 4x

we can start by simplifying the left side of the equation.

Step 1: Simplify the left side of the equation

To simplify the left side, we can first divide each term by -4x.

24x^4 / -4x = -6x^3
-12x^3 / -4x = 3x^2
48x^2 / -4x = -12x

So now the left side of the equation becomes:

-6x^3 + 3x^2 - 12x

Step 2: Rearrange the equation

Now let's rearrange the equation by moving all the terms to one side:

-6x^3 + 3x^2 - 12x = 6x^3 - 3x^2 - 4x

By adding 6x^3 to both sides, we get:

0 = 12x^3 - 3x^2 - 4x + 6x^3 - 3x^2 - 12x

Combining like terms, we have:

0 = 18x^3 - 6x^2 - 16x

Step 3: Factor out the common terms

To solve this equation further, we can factor out the common terms on the right side.

0 = 2x (9x^2 - 3x - 8)

Now, we can solve each factor separately.

First factor:

2x = 0
By dividing both sides by 2, we get:
x = 0

Second factor:

9x^2 - 3x - 8 = 0

We can use factoring, completing the square, or the quadratic formula to solve the quadratic equation. Let's use factoring in this case.

To factorize 9x^2 - 3x - 8, we need to find two numbers whose product is -72 (-8 * 9) and whose sum is -3. After checking several possibilities, we find that the numbers are -9 and 8.

Splitting the middle term, we have:

9x^2 - 9x + 8x - 8 = 0

Next, group the terms:

(9x^2 - 9x) + (8x - 8) = 0

Now factor by grouping:

9x(x - 1) + 8(x - 1) = 0

Factoring out the common factor, we get:

(9x + 8)(x - 1) = 0

Setting each factor equal to zero:

9x + 8 = 0
x - 1 = 0

Solving for x gives us:

9x = -8
x = -8/9

x = 1

So the solutions to the equation are:

x = 0, -8/9, 1