To find an expression equivalent to \((x-5)(2x+3)\), we can expand the expression using the distributive property (also known as the FOIL method for binomials).
-
Multiply the first terms:
\(x \cdot 2x = 2x^2\) -
Multiply the outer terms:
\(x \cdot 3 = 3x\) -
Multiply the inner terms:
\(-5 \cdot 2x = -10x\) -
Multiply the last terms:
\(-5 \cdot 3 = -15\)
Now, combine these results:
\[ 2x^2 + 3x - 10x - 15 \]
Combine like terms:
\[ 2x^2 + (3x - 10x) - 15 = 2x^2 - 7x - 15 \]
Thus, the expression equivalent to \((x-5)(2x+3)\) is:
\[ \boxed{2x^2 - 7x - 15} \]