Question

%7D%20%2B%2030%29%20" id="TexFormula1" title=" {40a}^{2} + 20a - 30 = ( - 1)( {15a}^{3} + 30) " alt=" {40a}^{2} + 20a - 30 = ( - 1)( {15a}^{3} + 30) " align="absmiddle" class="latex-formula">
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Answer 1

$\bf 40a^2+20a-30=(-1)(15a^3+30)\implies 40a^2+20a~~\begin{matrix} -30 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=-15a^3~~\begin{matrix} -30 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \\\\\\ 40a^2+20a=-15a^3\implies 15a^3+40a^2+20a=0\implies 5a(3a^2+8a+4)=0 \\\\\\ 5a(3a+2)(a+2)=0\implies a= \begin{cases} 0\\ -\frac{2}{3}\\ -2 \end{cases}$