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Simplifying 6e3 = 5e2 + 6e Reorder the terms: 6e3 = 6e + 5e2 Solving 6e3 = 6e + 5e2 Solving for variable 'e'. Reorder the terms: -6e + -5e2 + 6e3 = 6e + 5e2 + -6e + -5e2 Reorder the terms: -6e + -5e2 + 6e3 = 6e + -6e + 5e2 + -5e2 Combine like terms: 6e + -6e = 0 -6e + -5e2 + 6e3 = 0 + 5e2 + -5e2 -6e + -5e2 + 6e3 = 5e2 + -5e2 Combine like terms: 5e2 + -5e2 = 0 -6e + -5e2 + 6e3 = 0 Factor out the Greatest Common Factor (GCF), 'e'. e(-6 + -5e + 6e2) = 0 Factor a trinomial. e((-2 + -3e)(3 + -2e)) = 0Subproblem 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 '(-2 + -3e)' equal to zero and attempt to solve: Simplifying -2 + -3e = 0 Solving -2 + -3e = 0 Move all terms containing e to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3e = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3e = 0 + 2 -3e = 0 + 2 Combine like terms: 0 + 2 = 2 -3e = 2 Divide each side by '-3'. e = -0.6666666667 Simplifying e = -0.6666666667Subproblem 3
Set the factor '(3 + -2e)' equal to zero and attempt to solve: Simplifying 3 + -2e = 0 Solving 3 + -2e = 0 Move all terms containing e to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2e = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2e = 0 + -3 -2e = 0 + -3 Combine like terms: 0 + -3 = -3 -2e = -3 Divide each side by '-2'. e = 1.5 Simplifying e = 1.5Solution
e = {0, -0.6666666667, 1.5}
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