Multiply each term of $ \left( \color{blue}{x-12}\right) $ by each term in $ \left( x-7\right) $.

$$ \left( \color{blue}{x-12}\right) \cdot \left( x-7\right) = x^2-7x-12x+84 $$

Combine like terms:

$$ x^2 \color{blue}{-7x} \color{blue}{-12x} +84 = x^2 \color{blue}{-19x} +84 $$

Multiply each term of $ \left( \color{blue}{x^2-19x+84}\right) $ by each term in $ \left( x+3\right) $.

$$ \left( \color{blue}{x^2-19x+84}\right) \cdot \left( x+3\right) = x^3+3x^2-19x^2-57x+84x+252 $$

Combine like terms:

$$ x^3+ \color{blue}{3x^2} \color{blue}{-19x^2} \color{red}{-57x} + \color{red}{84x} +252 = x^3 \color{blue}{-16x^2} + \color{red}{27x} +252 $$

Multiply each term of $ \left( \color{blue}{x^3-16x^2+27x+252}\right) $ by each term in $ \left( x+3\right) $.

$$ \left( \color{blue}{x^3-16x^2+27x+252}\right) \cdot \left( x+3\right) = x^4+3x^3-16x^3-48x^2+27x^2+81x+252x+756 $$

Combine like terms:

$$ x^4+ \color{blue}{3x^3} \color{blue}{-16x^3} \color{red}{-48x^2} + \color{red}{27x^2} + \color{green}{81x} + \color{green}{252x} +756 = \\ = x^4 \color{blue}{-13x^3} \color{red}{-21x^2} + \color{green}{333x} +756 $$

Multiply each term of $ \left( \color{blue}{x^4-13x^3-21x^2+333x+756}\right) $ by each term in $ \left( x+14\right) $.

$$ \left( \color{blue}{x^4-13x^3-21x^2+333x+756}\right) \cdot \left( x+14\right) = \\ = x^5+14x^4-13x^4-182x^3-21x^3-294x^2+333x^2+4662x+756x+10584 $$

Combine like terms:

$$ x^5+ \color{blue}{14x^4} \color{blue}{-13x^4} \color{red}{-182x^3} \color{red}{-21x^3} \color{green}{-294x^2} + \color{green}{333x^2} + \color{orange}{4662x} + \color{orange}{756x} +10584 = \\ = x^5+ \color{blue}{x^4} \color{red}{-203x^3} + \color{green}{39x^2} + \color{orange}{5418x} +10584 $$