multiply \left(7x^{2}-6x+5\right)\left(4x^{2}+6x-3\right)
To multiply these two polynomials, we need to use the distributive property multiple times.
We start by multiplying each term in the first polynomial by each term in the second polynomial:
(7x^2) * (4x^2) + (7x^2) * (6x) + (7x^2) * (-3) + (-6x) * (4x^2) + (-6x) * (6x) + (-6x) * (-3) + (5) * (4x^2) + (5) * (6x) + (5) * (-3)
Now, simplify each of these products:
28x^4 + 42x^3 - 21x^2 - 24x^3 - 36x^2 + 18x + 20x^2 + 30x - 15
Finally, combine like terms to get the final answer:
28x^4 + 18x^3 - 5x^2 + 48x - 15