Factor $$ -6 x^{4}+8 x^{2}+8 $$ completely

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Factor the expression $$ -6x^4+8x^2+8 $$.
Factor the expression by following steps:
- step0: Factor:
  $$-6x^{4}+8x^{2}+8$$
- step1: Factor the expression:
  $$-2\left(3x^{4}+2x^{2}-6x^{2}-4\right)$$
- step2: Factor the expression:
  $$-2\left(x^{2}\left(3x^{2}+2\right)-2\left(3x^{2}+2\right)\right)$$
- step3: Factor the expression:
  $$-2\left(x^{2}-2\right)\left(3x^{2}+2\right)$$
The complete factorization of the expression $$ -6x^{4}+8x^{2}+8 $$ is $$ -2(x^{2}-2)(3x^{2}+2) $$.
The expression $$ -6x^{4}+8x^{2}+8 $$ factors completely to $$ -2(x^{2}-2)(3x^{2}+2) $$.

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