Answer:
To solve the equation \(2x^3 + 234x^2 = 0\) for \(x\), you can factor out the common term \(2x^2\):
\[ 2x^2(x + 117) = 0 \]
Now, apply the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero and solve for \(x\):
1. \(2x^2 = 0\)
Divide both sides by 2:
\(x^2 = 0\)
Take the square root of both sides:
\(x = 0\)
2. \(x + 117 = 0\)
Subtract 117 from both sides:
\(x = -117\)
Therefore, the solutions for the equation \(2x^3 + 234x^2 = 0\) are \(x = 0\) and \(x = -117\).
