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Simplifying (1 + 2n4)(5 + -5n4) = 0 Multiply (1 + 2n4) * (5 + -5n4) (1(5 + -5n4) + 2n4 * (5 + -5n4)) = 0 ((5 * 1 + -5n4 * 1) + 2n4 * (5 + -5n4)) = 0 ((5 + -5n4) + 2n4 * (5 + -5n4)) = 0 (5 + -5n4 + (5 * 2n4 + -5n4 * 2n4)) = 0 (5 + -5n4 + (10n4 + -10n8)) = 0 Combine like terms: -5n4 + 10n4 = 5n4 (5 + 5n4 + -10n8) = 0 Solving 5 + 5n4 + -10n8 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(1 + n4 + -2n8) = 0 Factor a trinomial. 5((1 + -1n4)(1 + 2n4)) = 0 Factor a difference between two squares. 5(((1 + n2)(1 + -1n2))(1 + 2n4)) = 0 Factor a difference between two squares. 5(((1 + n2)((1 + n)(1 + -1n)))(1 + 2n4)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 2n4)' equal to zero and attempt to solve: Simplifying 1 + 2n4 = 0 Solving 1 + 2n4 = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2n4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n4 = 0 + -1 2n4 = 0 + -1 Combine like terms: 0 + -1 = -1 2n4 = -1 Divide each side by '2'. n4 = -0.5 Simplifying n4 = -0.5 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 '(1 + n2)' equal to zero and attempt to solve: Simplifying 1 + n2 = 0 Solving 1 + n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n2 = 0 + -1 n2 = 0 + -1 Combine like terms: 0 + -1 = -1 n2 = -1 Simplifying n2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Subproblem 4
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-1, 1}
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