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Simplifying (an + 1)(2n + 6) = 0 Reorder the terms: (1 + an)(2n + 6) = 0 Reorder the terms: (1 + an)(6 + 2n) = 0 Multiply (1 + an) * (6 + 2n) (1(6 + 2n) + an(6 + 2n)) = 0 ((6 * 1 + 2n * 1) + an(6 + 2n)) = 0 ((6 + 2n) + an(6 + 2n)) = 0 (6 + 2n + (6 * an + 2n * an)) = 0 (6 + 2n + (6an + 2an2)) = 0 Reorder the terms: (6 + 6an + 2an2 + 2n) = 0 (6 + 6an + 2an2 + 2n) = 0 Solving 6 + 6an + 2an2 + 2n = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 6an + 2an2 + -6 + 2n = 0 + -6 Reorder the terms: 6 + -6 + 6an + 2an2 + 2n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6an + 2an2 + 2n = 0 + -6 6an + 2an2 + 2n = 0 + -6 Combine like terms: 0 + -6 = -6 6an + 2an2 + 2n = -6 Add '-2n' to each side of the equation. 6an + 2an2 + 2n + -2n = -6 + -2n Combine like terms: 2n + -2n = 0 6an + 2an2 + 0 = -6 + -2n 6an + 2an2 = -6 + -2n Reorder the terms: 6 + 6an + 2an2 + 2n = -6 + -2n + 6 + 2n Reorder the terms: 6 + 6an + 2an2 + 2n = -6 + 6 + -2n + 2n Combine like terms: -6 + 6 = 0 6 + 6an + 2an2 + 2n = 0 + -2n + 2n 6 + 6an + 2an2 + 2n = -2n + 2n Combine like terms: -2n + 2n = 0 6 + 6an + 2an2 + 2n = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 3an + an2 + n) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 3an + an2 + n)' equal to zero and attempt to solve: Simplifying 3 + 3an + an2 + n = 0 Solving 3 + 3an + an2 + n = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 3an + an2 + -3 + n = 0 + -3 Reorder the terms: 3 + -3 + 3an + an2 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3an + an2 + n = 0 + -3 3an + an2 + n = 0 + -3 Combine like terms: 0 + -3 = -3 3an + an2 + n = -3 Add '-1n' to each side of the equation. 3an + an2 + n + -1n = -3 + -1n Combine like terms: n + -1n = 0 3an + an2 + 0 = -3 + -1n 3an + an2 = -3 + -1n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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