Question 169893
Start by moving all the terms to one side:
5z^2 = 2z + 3
Subtracting both sides by 2z+3:
5z^2 - 2z - 3 = 0
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Always attempt to factor first, then failing that use the quadratic equation.
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In this case, you must use the quadratic equation.  Doing so will yield:
z = {1, -0.6}
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Details of quadratic below:
*[invoke quadratic "z", 5, -2, -3 ]