Answer:
x = 0 and x = 7/3
Step-by-step explanation:
The quadratic equation 9x^2 = 21x must first be rewritten in standard form, with one side being zero, to be factored.
21x is subtracted from both sides to arrive at 9x^2 - 21x = 0.
The next step is to factor out 3x, the most significant common factor (GCF): 3x(3x-7) = 0.
We now have two factors multiplied by one that equals zero. This indicates that for the expression to be zero overall, at least one element must be zero under the zero-product condition.
Our two options when we set all factors to zero are as follows:
1. 3x = 0
x = 0
2. 3x - 7 = 0
3x = 7
x = 7/3
Thus, x = 0 and x = 7/3 are the factored solutions to the quadratic equation 9x^2 = 21x.
