Multiply $ \color{blue}{3} $ by $ \left( x+6\right) $ $$ \color{blue}{3} \cdot \left( x+6\right) = 3x+18 $$

Multiply each term of $ \left( \color{blue}{3x+18}\right) $ by each term in $ \left( x-5\right) $.

$$ \left( \color{blue}{3x+18}\right) \cdot \left( x-5\right) = 3x^2-15x+18x-90 $$

Combine like terms:

$$ 3x^2 \color{blue}{-15x} + \color{blue}{18x} -90 = 3x^2+ \color{blue}{3x} -90 $$

Multiply each term of $ \left( \color{blue}{3x^2+3x-90}\right) $ by each term in $ \left( x-5\right) $.

$$ \left( \color{blue}{3x^2+3x-90}\right) \cdot \left( x-5\right) = 3x^3-15x^2+3x^2-15x-90x+450 $$

Combine like terms:

$$ 3x^3 \color{blue}{-15x^2} + \color{blue}{3x^2} \color{red}{-15x} \color{red}{-90x} +450 = 3x^3 \color{blue}{-12x^2} \color{red}{-105x} +450 $$

Multiply each term of $ \left( \color{blue}{3x^3-12x^2-105x+450}\right) $ by each term in $ \left( 3x-2\right) $.

$$ \left( \color{blue}{3x^3-12x^2-105x+450}\right) \cdot \left( 3x-2\right) = 9x^4-6x^3-36x^3+24x^2-315x^2+210x+1350x-900 $$

Combine like terms:

$$ 9x^4 \color{blue}{-6x^3} \color{blue}{-36x^3} + \color{red}{24x^2} \color{red}{-315x^2} + \color{green}{210x} + \color{green}{1350x} -900 = \\ = 9x^4 \color{blue}{-42x^3} \color{red}{-291x^2} + \color{green}{1560x} -900 $$

Multiply each term of $ \left( \color{blue}{9x^4-42x^3-291x^2+1560x-900}\right) $ by each term in $ \left( 3x-2\right) $.

$$ \left( \color{blue}{9x^4-42x^3-291x^2+1560x-900}\right) \cdot \left( 3x-2\right) = \\ = 27x^5-18x^4-126x^4+84x^3-873x^3+582x^2+4680x^2-3120x-2700x+1800 $$

Combine like terms:

$$ 27x^5 \color{blue}{-18x^4} \color{blue}{-126x^4} + \color{red}{84x^3} \color{red}{-873x^3} + \color{green}{582x^2} + \color{green}{4680x^2} \color{orange}{-3120x} \color{orange}{-2700x} +1800 = \\ = 27x^5 \color{blue}{-144x^4} \color{red}{-789x^3} + \color{green}{5262x^2} \color{orange}{-5820x} +1800 $$

Multiply each term of $ \left( \color{blue}{27x^5-144x^4-789x^3+5262x^2-5820x+1800}\right) $ by each term in $ \left( 3x-2\right) $.

$$ \left( \color{blue}{27x^5-144x^4-789x^3+5262x^2-5820x+1800}\right) \cdot \left( 3x-2\right) = \\ = 81x^6-54x^5-432x^5+288x^4-2367x^4+1578x^3+15786x^3-10524x^2-17460x^2+11640x+5400x-3600 $$

Combine like terms:

$$ 81x^6 \color{blue}{-54x^5} \color{blue}{-432x^5} + \color{red}{288x^4} \color{red}{-2367x^4} + \color{green}{1578x^3} + \color{green}{15786x^3} \color{orange}{-10524x^2} \color{orange}{-17460x^2} + \color{blue}{11640x} + \color{blue}{5400x} -3600 = \\ = 81x^6 \color{blue}{-486x^5} \color{red}{-2079x^4} + \color{green}{17364x^3} \color{orange}{-27984x^2} + \color{blue}{17040x} -3600 $$