Solve −3x2+30x−27=0−3𝑥2+30𝑥−27=0 for x𝑥 by first taking out a common factor. Enter the smaller number first.

First, we can factor out a -3 from each term in the equation:

-3(x² - 10x + 9) = 0

Next, we can set the equation inside the parentheses equal to zero (since if a product equals zero, at least one of the factors must be zero):

x² - 10x + 9 = 0

This is a quadratic equation in the form ax² + bx + c = 0. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, the equation factors easily:

(x - 1)(x - 9) = 0

Setting each factor equal to zero gives the solutions x = 1 and x = 9. So, the solutions to the original equation are x = 1 and x = 9. The smaller number is 1.