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To solve the equation:

\[
4x^2 + 72 = 6x^2
\]

we'll go through the following steps:

1. **Isolate the variable term**:
   
   Subtract \( 4x^2 \) from both sides:
   
   \[
   72 = 6x^2 - 4x^2
   \]
   
   Simplifying gives:
   
   \[
   72 = 2x^2
   \]

2. **Solve for \( x^2 \)**:
   
   Divide both sides by 2:
   
   \[
   36 = x^2
   \]
   
3. **Take the square root of both sides**:
   
   \[
   x = \pm \sqrt{36}
   \]
   
   \[
   x = \pm 6
   \]

So, the solutions for \( x \) are \( x = 6 \) or \( x = -6 \).

Would you like more details, or have any questions?

### Related Questions
1. What would the solution look like if the equation was \( 4x^2 + 72 = 8x^2 \)?
2. How do you solve an equation like \( 3x^2 + 50 = 5x^2 \)?
3. What happens if there are additional terms in \( x \), such as \( 4x^2 + 5x + 72 = 6x^2 \)?
4. What if the equation had a different power, for instance \( 4x^3 + 72 = 6x^3 \)?
5. How can we check if a given solution is correct for this equation?

### Tip:
For quadratic equations like this, always try to simplify by moving all terms involving \( x \) to one side to see if you can easily isolate \( x^2 \).

Learn how to solve the equation 4x^2 + 72 = 6x^2 with step-by-step instructions. This example demonstrates how to isolate x^2, divide terms, and take the square root to find solutions. Ideal for students in Grades 7-9 studying quadratic equations and algebra.

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