Step 1: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 21 , b = 41 ~ \text{ and } ~ c = 18 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 21 }$ by the constant term $\color{blue}{c = 18} $.

$$ a \cdot c = 378 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 378 $ and add to $ b = 41 $.

Step 4: All pairs of numbers with a product of $ 378 $ are:

PRODUCT = 378
1     378	-1     -378
2     189	-2     -189
3     126	-3     -126
6     63	-6     -63
7     54	-7     -54
9     42	-9     -42
14     27	-14     -27
18     21	-18     -21

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 41 }$

PRODUCT = 378 and SUM = 41
1     378	-1     -378
2     189	-2     -189
3     126	-3     -126
6     63	-6     -63
7     54	-7     -54
9     42	-9     -42
14     27	-14     -27
18     21	-18     -21

Step 6: Replace middle term $ 41 x $ with $ 27x+14x $:

$$ 21x^{2}+41x+18 = 21x^{2}+27x+14x+18 $$

Step 7: Apply factoring by grouping. Factor $ 3x $ out of the first two terms and $ 2 $ out of the last two terms.

$$ 21x^{2}+27x+14x+18 = 3x\left(7x+9\right) + 2\left(7x+9\right) = \left(3x+2\right) \left(7x+9\right) $$

Polynomial Factoring Calculator