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Simplifying 4(2e + 3e2) + 6(-3e + -4e2) = 0 (2e * 4 + 3e2 * 4) + 6(-3e + -4e2) = 0 (8e + 12e2) + 6(-3e + -4e2) = 0 8e + 12e2 + (-3e * 6 + -4e2 * 6) = 0 8e + 12e2 + (-18e + -24e2) = 0 Reorder the terms: 8e + -18e + 12e2 + -24e2 = 0 Combine like terms: 8e + -18e = -10e -10e + 12e2 + -24e2 = 0 Combine like terms: 12e2 + -24e2 = -12e2 -10e + -12e2 = 0 Solving -10e + -12e2 = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), '-2e'. -2e(5 + 6e) = 0 Ignore the factor -2.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 '(5 + 6e)' equal to zero and attempt to solve: Simplifying 5 + 6e = 0 Solving 5 + 6e = 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 + 6e = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6e = 0 + -5 6e = 0 + -5 Combine like terms: 0 + -5 = -5 6e = -5 Divide each side by '6'. e = -0.8333333333 Simplifying e = -0.8333333333Solution
e = {0, -0.8333333333}
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