Solve the Quadratic Equation: -9x + 3x² = 0

To solve the equation $-9x + 3x^2 = 0$, follow these steps:

Step 1: Factor the equation.

Observe that both terms in the equation share a common factor, $3x$. We can factor this out:

$-9x + 3x^2 = 3x(-3 + x)$.

The factored equation is $3x(-3 + x) = 0$.

Step 2: Apply the zero product property.

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. This gives us two equations to solve:

• $3x = 0$
• $-3 + x = 0$

Step 3: Solve each equation.

• For $3x = 0$, divide both sides by 3 to solve for $x$:
• $x = 0$
• For $-3 + x = 0$, add 3 to both sides to solve for $x$:
• $x = 3$

Therefore, the solutions to the equation $-9x + 3x^2 = 0$ are $x = 0$ and $x = 3$.

Matching these solutions to the given choices, the correct answer is choice 3: $x = 0, x = 3$.

Thus, the values of $x$ that satisfy the equation are $x = 0$ and $x = 3$.