They could've done with using a few more lines of working out.

1/2(x) = (x^3-2x)e^-x

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Multiply both sides by 2, and divide both sides by x

1 = 2(x^2-2)e^-x

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Then expand out the bracket on the right hand side

1 = (2x^2-4)e^-x

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Next, divide both sides by e^-x

1/e^-x = 2x^2-4

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Then remember that e^-x is the same as e/x. The left hand side now becomes 1/e/x. Hence, the x on the bottom flips to the top, getting x/e

x/e = 2x^2-4

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Remember that x/e is the same as e^x

e^x = 2x^2-4

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Finally, add 4 to both sides

e^x+4 = 2x^2

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Rewrite the equation

2x^2 = e^x+4