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:

$$ a = 8 , b = -14 ~ \text{ and } ~ c = 3 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 8 }$ by the constant term $\color{blue}{c = 3} $.

$$ a \cdot c = 24 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 24 $ and add to $ b = -14 $.

Step 4: All pairs of numbers with a product of $ 24 $ are:

PRODUCT = 24
1     24	-1     -24
2     12	-2     -12
3     8	-3     -8
4     6	-4     -6

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -14 }$

PRODUCT = 24 and SUM = -14
1     24	-1     -24
2     12	-2     -12
3     8	-3     -8
4     6	-4     -6

Step 6: Replace middle term $ -14 x $ with $ -2x-12x $:

$$ 8x^{2}-14x+3 = 8x^{2}-2x-12x+3 $$

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

$$ 8x^{2}-2x-12x+3 = 2x\left(4x-1\right) -3\left(4x-1\right) = \left(2x-3\right) \left(4x-1\right) $$

Polynomial Factoring Calculator