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Simplifying 143n3 + -41n2 = 30n2 + 30n Reorder the terms: -41n2 + 143n3 = 30n2 + 30n Reorder the terms: -41n2 + 143n3 = 30n + 30n2 Solving -41n2 + 143n3 = 30n + 30n2 Solving for variable 'n'. Reorder the terms: -30n + -41n2 + -30n2 + 143n3 = 30n + 30n2 + -30n + -30n2 Combine like terms: -41n2 + -30n2 = -71n2 -30n + -71n2 + 143n3 = 30n + 30n2 + -30n + -30n2 Reorder the terms: -30n + -71n2 + 143n3 = 30n + -30n + 30n2 + -30n2 Combine like terms: 30n + -30n = 0 -30n + -71n2 + 143n3 = 0 + 30n2 + -30n2 -30n + -71n2 + 143n3 = 30n2 + -30n2 Combine like terms: 30n2 + -30n2 = 0 -30n + -71n2 + 143n3 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-30 + -71n + 143n2) = 0 Factor a trinomial. n((-3 + -11n)(10 + -13n)) = 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 '(-3 + -11n)' equal to zero and attempt to solve: Simplifying -3 + -11n = 0 Solving -3 + -11n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -11n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -11n = 0 + 3 -11n = 0 + 3 Combine like terms: 0 + 3 = 3 -11n = 3 Divide each side by '-11'. n = -0.2727272727 Simplifying n = -0.2727272727Subproblem 3
Set the factor '(10 + -13n)' equal to zero and attempt to solve: Simplifying 10 + -13n = 0 Solving 10 + -13n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -13n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -13n = 0 + -10 -13n = 0 + -10 Combine like terms: 0 + -10 = -10 -13n = -10 Divide each side by '-13'. n = 0.7692307692 Simplifying n = 0.7692307692Solution
n = {0, -0.2727272727, 0.7692307692}
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