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Simplifying 4x(n + 2) * x(n + 5) = 0 Reorder the terms: 4x(2 + n) * x(n + 5) = 0 Reorder the terms: 4x(2 + n) * x(5 + n) = 0 Reorder the terms for easier multiplication: 4x * x(2 + n)(5 + n) = 0 Multiply x * x 4x2(2 + n)(5 + n) = 0 Multiply (2 + n) * (5 + n) 4x2(2(5 + n) + n(5 + n)) = 0 4x2((5 * 2 + n * 2) + n(5 + n)) = 0 4x2((10 + 2n) + n(5 + n)) = 0 4x2(10 + 2n + (5 * n + n * n)) = 0 4x2(10 + 2n + (5n + n2)) = 0 Combine like terms: 2n + 5n = 7n 4x2(10 + 7n + n2) = 0 (10 * 4x2 + 7n * 4x2 + n2 * 4x2) = 0 Reorder the terms: (28nx2 + 4n2x2 + 40x2) = 0 (28nx2 + 4n2x2 + 40x2) = 0 Solving 28nx2 + 4n2x2 + 40x2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(7n + n2 + 10) = 0 Factor a trinomial. 4x2((n + 2)(n + 5)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 = 0 + -1x2 Remove the zero: 0 = -1x2 Simplifying 0 = -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(n + 2)' equal to zero and attempt to solve: Simplifying n + 2 = 0 Reorder the terms: 2 + n = 0 Solving 2 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 3
Set the factor '(n + 5)' equal to zero and attempt to solve: Simplifying n + 5 = 0 Reorder the terms: 5 + n = 0 Solving 5 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Solution
n = {-2, -5}
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