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Solve 3x2−15x=0

by factoring out the greatest common factor. Enter your solutions as an integer.(2 points)
x =


x=

1 answer

To solve the equation \( 3x^2 - 15x = 0 \) by factoring out the greatest common factor (GCF), follow these steps:

  1. Identify the GCF of the terms \( 3x^2 \) and \( -15x \). The GCF is \( 3x \).

  2. Factor out \( 3x \) from the equation: \[ 3x(x - 5) = 0 \]

  3. Set each factor equal to zero: \[ 3x = 0 \quad \text{or} \quad x - 5 = 0 \]

  4. Solve for \( x \):

    • From \( 3x = 0 \): \[ x = 0 \]
    • From \( x - 5 = 0 \): \[ x = 5 \]

Thus, the solutions are:

  • \( x = 0 \)
  • \( x = 5 \)

So the final answers are:

x = 0

x = 5