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Simplifying 4e(e + 6) = e + -15 Reorder the terms: 4e(6 + e) = e + -15 (6 * 4e + e * 4e) = e + -15 (24e + 4e2) = e + -15 Reorder the terms: 24e + 4e2 = -15 + e Solving 24e + 4e2 = -15 + e Solving for variable 'e'. Reorder the terms: 15 + 24e + -1e + 4e2 = -15 + e + 15 + -1e Combine like terms: 24e + -1e = 23e 15 + 23e + 4e2 = -15 + e + 15 + -1e Reorder the terms: 15 + 23e + 4e2 = -15 + 15 + e + -1e Combine like terms: -15 + 15 = 0 15 + 23e + 4e2 = 0 + e + -1e 15 + 23e + 4e2 = e + -1e Combine like terms: e + -1e = 0 15 + 23e + 4e2 = 0 Factor a trinomial. (5 + e)(3 + 4e) = 0Subproblem 1
Set the factor '(5 + e)' equal to zero and attempt to solve: Simplifying 5 + e = 0 Solving 5 + e = 0 Move all terms containing e to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + e = 0 + -5 Combine like terms: 5 + -5 = 0 0 + e = 0 + -5 e = 0 + -5 Combine like terms: 0 + -5 = -5 e = -5 Simplifying e = -5Subproblem 2
Set the factor '(3 + 4e)' equal to zero and attempt to solve: Simplifying 3 + 4e = 0 Solving 3 + 4e = 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 + 4e = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4e = 0 + -3 4e = 0 + -3 Combine like terms: 0 + -3 = -3 4e = -3 Divide each side by '4'. e = -0.75 Simplifying e = -0.75Solution
e = {-5, -0.75}
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