To factorize \(6x^2 + 7x - 20\), we need to find two numbers that multiply to -120 (the product of the leading coefficient, 6, and the constant, -20) and add up to the coefficient of the middle term, 7. These numbers are 15 and -8.
Therefore, we can write:
\begin{align*}
6x^2 + 7x - 20 &= 6x^2 + 15x - 8x - 20 \\
&= 3x(2x+5) - 4(2x+5) \\
&= (3x-4)(2x+5)
\end{align*}
So the factorization of \(6x^2 + 7x - 20\) is \((3x-4)(2x+5)\).