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Solving Linear Equations Using Transpose of Terms

Solve: 6x2 ...

Question

Solve: $(6 x^{2} - 3 x - 3) + (x^{2} - 3 x + 2) =$

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Solution

$(6 x^{2} - 3 x - 3) + (x^{2} - 3 x + 2)$
$= 3 (2 x^{2} - x - 1) + (x^{2} - 3 x + 2)$
$= 3 (2 x^{2} - 2 x + x - 1) + (x^{2} - 2 x - x + 2)$
$= 3 (2 x (x - 1) + 1 (x - 1)) + (x (x - 2) - 1 (x - 2))$
$= 3 (x - 1) (2 x + 1) + (x - 2) (x - 1)$
$= (x - 1) (3 (2 x + 1) + x - 2)$
$= (x - 1) (6 x + 3 + x - 2)$
$= (x - 1) (7 x + 1)$
$∴ (6 x^{2} - 3 x - 3) + (x^{2} - 3 x + 2) = (x - 1) (7 x + 1)$ .

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