Question

$2x + 2 = 4x {}^{2} \: \: find \: the \: value \: of \: x$
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Answer 1

$2x + 2 = 4x {}^{2} \\ = 2x + 2 - 4x {}^{2} = 0 \\ = 2 + 2x - 4x {}^{2} = 0 \\ = 2 + 4x - 2x - 4x {}^{2} = 0 \\ = 2(1 + 2x) - 2x(1 + 2x) = 0 \\ = (2 - 2x)(1 + 2x)$

$either \: \\ \\ 2 - 2x = 0 \\ = - 2x = 2 \\ x = \frac{2}{ - 2} \\ x = - 1$

$or \: 1 + 2x = 0 \\ 2x = - 1 \\ x = \frac{ - 1}{2}$