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Simplifying (4n + -5)(3n + 8) + -1(3n + -11) = 12n2 + Bn + -29 Reorder the terms: (-5 + 4n)(3n + 8) + -1(3n + -11) = 12n2 + Bn + -29 Reorder the terms: (-5 + 4n)(8 + 3n) + -1(3n + -11) = 12n2 + Bn + -29 Multiply (-5 + 4n) * (8 + 3n) (-5(8 + 3n) + 4n * (8 + 3n)) + -1(3n + -11) = 12n2 + Bn + -29 ((8 * -5 + 3n * -5) + 4n * (8 + 3n)) + -1(3n + -11) = 12n2 + Bn + -29 ((-40 + -15n) + 4n * (8 + 3n)) + -1(3n + -11) = 12n2 + Bn + -29 (-40 + -15n + (8 * 4n + 3n * 4n)) + -1(3n + -11) = 12n2 + Bn + -29 (-40 + -15n + (32n + 12n2)) + -1(3n + -11) = 12n2 + Bn + -29 Combine like terms: -15n + 32n = 17n (-40 + 17n + 12n2) + -1(3n + -11) = 12n2 + Bn + -29 Reorder the terms: -40 + 17n + 12n2 + -1(-11 + 3n) = 12n2 + Bn + -29 -40 + 17n + 12n2 + (-11 * -1 + 3n * -1) = 12n2 + Bn + -29 -40 + 17n + 12n2 + (11 + -3n) = 12n2 + Bn + -29 Reorder the terms: -40 + 11 + 17n + -3n + 12n2 = 12n2 + Bn + -29 Combine like terms: -40 + 11 = -29 -29 + 17n + -3n + 12n2 = 12n2 + Bn + -29 Combine like terms: 17n + -3n = 14n -29 + 14n + 12n2 = 12n2 + Bn + -29 Reorder the terms: -29 + 14n + 12n2 = -29 + nB + 12n2 Add '29' to each side of the equation. -29 + 14n + 29 + 12n2 = -29 + nB + 29 + 12n2 Reorder the terms: -29 + 29 + 14n + 12n2 = -29 + nB + 29 + 12n2 Combine like terms: -29 + 29 = 0 0 + 14n + 12n2 = -29 + nB + 29 + 12n2 14n + 12n2 = -29 + nB + 29 + 12n2 Reorder the terms: 14n + 12n2 = -29 + 29 + nB + 12n2 Combine like terms: -29 + 29 = 0 14n + 12n2 = 0 + nB + 12n2 14n + 12n2 = nB + 12n2 Add '-12n2' to each side of the equation. 14n + 12n2 + -12n2 = nB + 12n2 + -12n2 Combine like terms: 12n2 + -12n2 = 0 14n + 0 = nB + 12n2 + -12n2 14n = nB + 12n2 + -12n2 Combine like terms: 12n2 + -12n2 = 0 14n = nB + 0 14n = nB Solving 14n = nB Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1nB' to each side of the equation. 14n + -1nB = nB + -1nB Combine like terms: nB + -1nB = 0 14n + -1nB = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(14 + -1B) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(14 + -1B)' equal to zero and attempt to solve: Simplifying 14 + -1B = 0 Solving 14 + -1B = 0 Move all terms containing n to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1B = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1B = 0 + -14 -1B = 0 + -14 Combine like terms: 0 + -14 = -14 -1B = -14 Add 'B' to each side of the equation. -1B + B = -14 + B Combine like terms: -1B + B = 0 0 = -14 + B Simplifying 0 = -14 + B The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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