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.
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.