$7{x}^{2}+3x-54$

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Split the second term in

7{x}^{2}+3x-54

into two terms.

Multiply the coefficient of the first term by the constant term.

7\times -54=-378

Ask: Which two numbers add up to

3

and multiply to

-378

21

and

-18

Split

3x

as the sum of

21x

and

-18x

7{x}^{2}+21x-18x-54

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7{x}^{2}+21x-18x-54

Factor out common terms in the first two terms, then in the last two terms.

7x(x+3)-18(x+3)

Factor out the common term

x+3

(x+3)(7x-18)

Done

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7x2+3x−547{x}^{2}+3x-547x2+3x−54