Answer:
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).
