Solve {l}{3(5-3x)^2+4(5-3x)-2}{3*(25-9x^2)+4+20-12x}

$$\left. \begin{array} { l } { 3 ( 5 - 3 x ) ^ { 2 } + 4 ( 5 - 3 x ) - 2 } \\ { 3 \cdot ( 25 - 9 x ^ { 2 } ) + 4 + 20 - 12 x } \end{array} \right.$$

Least Common Multiple

$$\frac{\left(\left(9x-17\right)^{2}-10\right)\left(\left(9x+2\right)^{2}-301\right)}{27}$$

Solution Steps

Factor the expressions that are not already factored.

$$-102x+27x^{2}+93=3\times 9\left(x-\left(-\frac{1}{9}\sqrt{10}+\frac{17}{9}\right)\right)\left(x-\left(\frac{1}{9}\sqrt{10}+\frac{17}{9}\right)\right) 99-12x-27x^{2}=-3\times 9\left(x-\left(-\frac{1}{9}\sqrt{301}-\frac{2}{9}\right)\right)\left(x-\left(\frac{1}{9}\sqrt{301}-\frac{2}{9}\right)\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$243\left(x-\frac{-\sqrt{301}-2}{9}\right)\left(x-\frac{17-\sqrt{10}}{9}\right)\left(x-\frac{\sqrt{301}-2}{9}\right)\left(x-\frac{\sqrt{10}+17}{9}\right)$$

Expand the expression.

$$243x^{4}-810x^{3}-462x^{2}+3738x-3069$$

Evaluate

$$27x^{2}-102x+93,\ 99-12x-27x^{2}$$