Ineed to know how to solve linear equations with two of the same variable on one side, like this equation: 9x^2-39x=168
either that or if anyone knows, using the zero product property on trinomial quadratic equations.
!
-dylan

The zeroes are at (-8/3, 0) and (7, 0).

Step-by-step explanation:

Your equation is 9x² - 39x = 168

1. Put the equation into standard form

Subtract 168 from each side.

9x² - 39x - 168 = 0

2. Remove the common factor

Divide each side the highest common factor of all coefficients (3).

3x² -13x - 56 = 0

Your equation has the form

ax² + bx +c = 0

a = 3; b = -13; c = -56

3. Factor the quadratic

a. Multiply a·c: 3(-56) = -168

b. List all the factors of ac: 1, 2, 3, 4, 6, 7, 8, 12, 21, 24, 28, 42, 56, 84, 168

c. Find two numbers whose sum = b  and whose product = ac.

   8 and -21 work, because 8 - 21 = -13 and 8(-21) = -168

d. Rewrite -13x as 8x - 21x: 3x² + 8x - 21x -56 = 0

e. Factor by grouping: x(3x + 8) - 7(3x + 8) = (3x + 8)(x - 7) = 0

4. Solve the quadratic

(3x + 8)(x - 7) = 0

Use the zero product property: a product of factors is zero if one or more of the factors is zero.

3x + 8 = 0          x - 7 = 0

     3x = -8              x = 7

       x = -8/3

The zeroes are at (-8/3, 0) and (7, 0).