factorise- 14x2-9x-18?

14x^2 - 9x - 18
= 14x^2 + 12x - 21x - 18
= (14x^2 + 12x) - (21x + 18)
= 2x(7x + 6) - 3(7x + 6)
= (7x + 6)(2x - 3)

14x² - 9x - 18 = 0
x² - 9/14x = 9/7
x² - 9/28x = 9/7 + (- 9/28)²
x² - 9/28x = 1,008/784 + 81/784
(x - 9/28)² = 1,089/784
x - 9/28 = 33/28

Factors:
= x - 9/28 - 33/28, = x - 42/28, = x - 3/2, = 2x - 3
= x - 9/28 + 33/28, = x + 24/28, = x + 6/7, = 7x + 6

Answer: (2x - 3)(7x + 6) are the factors.

Proof (F.O.I.L. back to 14x² - 9x - 18):
= (2x - 3)(7x + 6)
= (2x * 7x) + (2x * 6) + (- 3 * 7x) + (- 3 * 6)
= 14x² + 12x - 21x - 18
= 14x² - 9x - 18

14x² - 9x - 18 = (2x - 3)(7x + 6)

14x^2-9x-18 = 14x^2 - 21x + 12x - 18
= 7x(2x - 3) + 6(2x - 3)
= (7x + 6)(2x - 3)
14x^2-9x-18 = (7x + 6)(2x - 3). Answer.

x=9+-(81+1008)^1/2/28=9+33/28=3/2 & 9-33/14=-24/28=-6/7
14(x-3/2)(x+6/7)=(2x-3)(7x+6)
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Double check;14x^2+12x-21x-18=14x^2-9x-18

Use the quadratic formula:
x = [-b+sqrt(b^2-4ac)]/2a
and
x = [-b-sqrt(b^2-4ac)]/2a
a = -14
b= -9
c = -18
get two values of
x = { 3/2 and -6/7}
therefore its factors are
(x -3/2)(x+6/7)