3x^2 = 75x

solve the quadratic equation by factoring.

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3x² = 75x

3x²-75x = 0

3x (x-25) = 0

Thus:

3x = 0

x = 0/3

and

x-25 = 0

x = 0 + 25

x = 25

x = 0 or 25

Step-by-step explanation:

In general, solving a polynomial by factoring requires it be put in the form ...

f (x) = 0

Here, we do that by subtracting the right side:

3x^2 - 75x = 0

Factoring gives ...

3x (x - 25) = 0

The zero product rule says the product can only be zero if one or more of the factors is zero. That will happen when ...

x = 0 or x = 25

The solutions are x = 0 or x = 25.