Final answer:
The zeroes of the equation x²+2ax-3bx-6ab=0 are found using the quadratic formula which applies to equations in the form ax²+bx+c = 0, with specific coefficients for a, b, and c.
Step-by-step explanation:
The zeroes of the quadratic equation x²+2ax-3bx-6ab=0 can be found using the quadratic formula. This is a standard method applied to any equation of the form ax²+bx+c = 0, where a, b, and c are coefficients and x represents the variable to be solved for.
For our given equation, the coefficients are a = 1, b = 2a-3b, and c = -6ab. Applying the quadratic formula (-b ± √(b² - 4ac)) / (2a) we can find the two possible zeroes of the equation.