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Simplifying (3e + 2)(2e + -4) = 0 Reorder the terms: (2 + 3e)(2e + -4) = 0 Reorder the terms: (2 + 3e)(-4 + 2e) = 0 Multiply (2 + 3e) * (-4 + 2e) (2(-4 + 2e) + 3e * (-4 + 2e)) = 0 ((-4 * 2 + 2e * 2) + 3e * (-4 + 2e)) = 0 ((-8 + 4e) + 3e * (-4 + 2e)) = 0 (-8 + 4e + (-4 * 3e + 2e * 3e)) = 0 (-8 + 4e + (-12e + 6e2)) = 0 Combine like terms: 4e + -12e = -8e (-8 + -8e + 6e2) = 0 Solving -8 + -8e + 6e2 = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -4e + 3e2) = 0 Factor a trinomial. 2((-2 + -3e)(2 + -1e)) = 0 Ignore the factor 2.Subproblem 1
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 2
Set the factor '(2 + -1e)' equal to zero and attempt to solve: Simplifying 2 + -1e = 0 Solving 2 + -1e = 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 + -1e = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1e = 0 + -2 -1e = 0 + -2 Combine like terms: 0 + -2 = -2 -1e = -2 Divide each side by '-1'. e = 2 Simplifying e = 2Solution
e = {-0.6666666667, 2}
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