High School

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Solve by factoring:

\[ 9x^3 - 48x^2 - 20x = 16x \]

Answer :

Answer: x = 0, x = 20, or x = 3/2

Explanation:

We can start by factoring out x from both sides of the equation:

9x^3 - 48x^2 - 20x - 16x = 0

x(9x^2 - 48x - 20 - 16) = 0

Simplifying the expression inside the parentheses:

x(9x^2 - 48x - 36) = 0

Now we can factor the quadratic expression inside the parentheses:

x(3x - 6)(3x - 6) = 0

Simplifying further:

x(3x - 6)^2 = 0

This equation has three solutions:

x = 0, x = 20, or x = 3/2.

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Rewritten by : Barada

Answer:

To solve the given equation by factoring, we first rearrange the terms to get:

9x^3 - 48x^2 - 36x = 0

We can factor out a common factor of 9x to obtain:

9x(x^2 - 5.33x - 4) = 0

Next, we can factor the quadratic expression inside the parentheses using the quadratic formula or by factoring by grouping. Using the quadratic formula, we have:

x = [5.33 ± sqrt(5.33^2 + 4(4))]/2

x = [5.33 ± sqrt(42.89)]/2

x = 4.85 or x = 0.48

Therefore, the solutions to the original equation are:

x = 0 (from the factor of 16x on the left-hand side of the equation)

x = 4.85

x = 0.48

Step-by-step explanation: