Factoring a quadratic trinomial

How do you factor 4x² - 4x - 3?

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4x² - 4x - 3
= 4x² - 6x + 2x - 3   {factoring by grouping, split -4x into -6x and 2x}
= 2x(2x - 3) + 1(2x - 3)  {factored 2x out of 1st 2 terms and 1 out of last 2 terms}
= (2x + 1)(2x - 3)   {factored 2x - 3 out of the two terms}

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