[tex](x - 2x + 3) \times (x ^{2} - 2x + 4) = 6[/tex]

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To solve this equation, we will first expand the left side of the equation:

[tex](x - 2x + 3) \times (x ^{2} - 2x + 4) = (x^3 - 2x^2 + 3x - 2x^2 + 4x - 6) = x^3 - 4x^2 + 7x - 6 = 6[/tex]

Now, we can simplify the equation:

[tex]x^3 - 4x^2 + 7x - 6 = 6[/tex]

Next, we will move all terms to one side of the equation:

[tex]x^3 - 4x^2 + 7x - 6 - 6 = 0[/tex]

[tex]x^3 - 4x^2 + 7x - 12 = 0[/tex]

This is a cubic equation that can be solved using various methods such as factoring, synthetic division, long division, or using numerical methods.