Solve the following by factoring: 3x^2-26x=9

Answer 1

To solve this equation by factoring, we first rearrange the equation to set it equal to zero:

3x^2 - 26x - 9 = 0

Next, we look for two numbers that multiply to -27 (3 * -9) and add to -26. The numbers are -27 and 1.

So, we rewrite the equation using these values:

3x^2 - 27x + x - 9 = 0
3x(x - 9) + 1(x - 9) = 0
(3x + 1)(x - 9) = 0

Setting each factor equal to zero, we get:

3x + 1 = 0
3x = -1
x = -1/3

and

x - 9 = 0
x = 9

Therefore, the solutions to the equation 3x^2 - 26x = 9 are x = -1/3 and x = 9.