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x^3=16x Find all real solutions
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x^3 - 16x = 0 x(x^2 - 16) = 0 this equation is true when x = 0 or when x^2 = 16 solutions: x = -4, 0, 4
\(\bf x^3=16x\implies x^3-16x=0\quad \textit{taking common factor}\\ \quad \\ x(x^2-16)=0\implies x(x^2-4^2)=0\qquad\\ \textit{recall that }\color{blue}{a^2-b^2 = (a-b)(a+b)}\\ \quad \\ x(x^2-4^2)=0\implies x(x-4)(x+4)=0\)
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