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Simplifying 40e2 + 10e + -20ef = 0 Reorder the terms: 10e + -20ef + 40e2 = 0 Solving 10e + -20ef + 40e2 = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), '10e'. 10e(1 + -2f + 4e) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'e' equal to zero and attempt to solve: Simplifying e = 0 Solving e = 0 Move all terms containing e to the left, all other terms to the right. Simplifying e = 0Subproblem 2
Set the factor '(1 + -2f + 4e)' equal to zero and attempt to solve: Simplifying 1 + -2f + 4e = 0 Reorder the terms: 1 + 4e + -2f = 0 Solving 1 + 4e + -2f = 0 Move all terms containing e to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 4e + -1 + -2f = 0 + -1 Reorder the terms: 1 + -1 + 4e + -2f = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4e + -2f = 0 + -1 4e + -2f = 0 + -1 Combine like terms: 0 + -1 = -1 4e + -2f = -1 Add '2f' to each side of the equation. 4e + -2f + 2f = -1 + 2f Combine like terms: -2f + 2f = 0 4e + 0 = -1 + 2f 4e = -1 + 2f Divide each side by '4'. e = -0.25 + 0.5f Simplifying e = -0.25 + 0.5fSolution
e = {0, -0.25 + 0.5f}
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