ANSWER
[tex]\begin{gathered} x\text{ = 0 (multiplicity of 2)} \\ x\text{ = }\sqrt[]{7}\text{ (multiplicity of 1)} \\ x\text{ = - }\sqrt[]{7}\text{ (multiplicity of 1)} \end{gathered}[/tex]
EXPLANATION
[tex]\begin{gathered} f(x)=-7x^2(x^2-7) \\ \text{set }-7x^2(x^2-7)\text{ = 0} \\ x^2\text{ = 0} \\ x\text{ = +-}\sqrt[]{0} \\ x\text{ = 0}\ldots\ldots..\ldots..\ldots\ldots.(1) \\ x^2\text{ - 7 = 0} \\ x^2\text{ = 7} \\ x\text{ = +-}\sqrt[]{7} \\ x\text{ = }\sqrt[]{7}\text{ or x = -}\sqrt[]{7}\ldots\ldots\ldots....\ldots\ldots\text{....}\mathrm{}.(2) \end{gathered}[/tex]
The final solution is all the values that make -7x^2(x^2 -7) = 0 true.
while the multiplicity of a root is the number of times the root appears.
for the multiplicity:
[tex]\begin{gathered} x\text{ = 0 (multiplicity of 2)} \\ x\text{ = }\sqrt[]{7}\text{ (multiplicity of 1)} \\ x\text{ = - }\sqrt[]{7}\text{ (multiplicity of 1)} \end{gathered}[/tex]
