College

We appreciate your visit to Solve the equation tex 6x 3 48x 4 90x 3 0 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Solve the equation:

[tex]\[ 6x^3 - 48x^4 + 90x^3 = 0 \][/tex]

Answer :

To solve the equation [tex]\(6x^3 - 48x^4 + 90x^3 = 0\)[/tex], let's break it down step-by-step:

1. Combine Like Terms: First, notice that the equation has two [tex]\(x^3\)[/tex] terms. Let's combine them. The equation becomes:
[tex]\[
(6x^3 + 90x^3) - 48x^4 = 0
\][/tex]
[tex]\[
96x^3 - 48x^4 = 0
\][/tex]

2. Factor the Equation: Next, we factor out the greatest common factor from each term, which is [tex]\(48x^3\)[/tex]:
[tex]\[
48x^3(2 - x) = 0
\][/tex]

3. Set Each Factor to Zero: This gives us two factors to consider, which we set to zero:
[tex]\[
48x^3 = 0 \quad \text{or} \quad (2 - x) = 0
\][/tex]

4. Solve Each Equation:
- For [tex]\(48x^3 = 0\)[/tex], divide both sides by 48:
[tex]\[
x^3 = 0 \quad \Rightarrow \quad x = 0
\][/tex]
- For [tex]\(2 - x = 0\)[/tex], add [tex]\(x\)[/tex] to both sides:
[tex]\[
2 = x \quad \Rightarrow \quad x = 2
\][/tex]

5. Solution: The solutions to the equation are [tex]\(x = 0\)[/tex] and [tex]\(x = 2\)[/tex].

Therefore, the equation [tex]\(6x^3 - 48x^4 + 90x^3 = 0\)[/tex] has solutions [tex]\(x = 0\)[/tex] and [tex]\(x = 2\)[/tex].

Thanks for taking the time to read Solve the equation tex 6x 3 48x 4 90x 3 0 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada