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Simplifying (3e + -32)(e + 16) * e = 0 Reorder the terms: (-32 + 3e)(e + 16) * e = 0 Reorder the terms: (-32 + 3e)(16 + e) * e = 0 Reorder the terms for easier multiplication: e(-32 + 3e)(16 + e) = 0 Multiply (-32 + 3e) * (16 + e) e(-32(16 + e) + 3e * (16 + e)) = 0 e((16 * -32 + e * -32) + 3e * (16 + e)) = 0 e((-512 + -32e) + 3e * (16 + e)) = 0 e(-512 + -32e + (16 * 3e + e * 3e)) = 0 e(-512 + -32e + (48e + 3e2)) = 0 Combine like terms: -32e + 48e = 16e e(-512 + 16e + 3e2) = 0 (-512 * e + 16e * e + 3e2 * e) = 0 (-512e + 16e2 + 3e3) = 0 Solving -512e + 16e2 + 3e3 = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), 'e'. e(-512 + 16e + 3e2) = 0 Factor a trinomial. e((-16 + -1e)(32 + -3e)) = 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 '(-16 + -1e)' equal to zero and attempt to solve: Simplifying -16 + -1e = 0 Solving -16 + -1e = 0 Move all terms containing e to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1e = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1e = 0 + 16 -1e = 0 + 16 Combine like terms: 0 + 16 = 16 -1e = 16 Divide each side by '-1'. e = -16 Simplifying e = -16Subproblem 3
Set the factor '(32 + -3e)' equal to zero and attempt to solve: Simplifying 32 + -3e = 0 Solving 32 + -3e = 0 Move all terms containing e to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + -3e = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -3e = 0 + -32 -3e = 0 + -32 Combine like terms: 0 + -32 = -32 -3e = -32 Divide each side by '-3'. e = 10.66666667 Simplifying e = 10.66666667Solution
e = {0, -16, 10.66666667}
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