#### Answer

$(2x-7)(2x+3)$

#### Work Step by Step

$4x^{2}-8x-21$
First, identify two numbers that multiply with each other to become -84, the product of the constant and coefficient of $x^{2}$ (4 $\times$ -21) and add together to become -8, the coefficient of x.
From inspection, we identify the numbers as 6 and -14.
Secondly split the coefficient of x into the sum of the two above numbers.
$4x^{2}-8x-21$
$=4x^{2}+(6-14)x-21$
$=4x^{2}+6x-14x-21$
Factorize by grouping to find the answer.
$4x^{2}+6x-14x-21$
$=2x(2x+3)-7(2x+3)$
$=(2x-7)(2x+3)$