`x^(3)+150=6x^(2)+25x`
What is the sum of all values of x that satisfy the equation above?

Answer

To solve the equation \( x^3 + 150 = 6x^2 + 25x \), we will first rewrite it in standard cubic form.

### Step 1: Rearrange the equation
We start by moving all terms to one side of the equation:
\[ x^3 - 6x^2 - 25x + 150 = 0 \]

### Step 2: Identify coefficients
In the standard form of a cubic equation \( ax^3 + bx^2 + cx + d = 0 \), we can identify:
- \( a = 1 \)
- \( b = -6 \)
- \( c = -25 \)
- \( d = 150 \)

### Step 3: Use the sum of roots formula
The sum of the roots of a polynomial can be calculated using the formula:
\[ \text{Sum of roots} = -\frac{b}{a} \]
Substituting the values of \( b \) and \( a \):
\[ \text{Sum of roots} = -\frac{-6}{1} = 6 \]

### Conclusion
The sum of all values of \( x \) that satisfy the equation is \( 6 \).

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