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Simplifying (3y5 + 8y + -10y2) + -1(-12y5 + 4y3 + 14n2) = 0 Reorder the terms: (8y + -10y2 + 3y5) + -1(-12y5 + 4y3 + 14n2) = 0 Remove parenthesis around (8y + -10y2 + 3y5) 8y + -10y2 + 3y5 + -1(-12y5 + 4y3 + 14n2) = 0 Reorder the terms: 8y + -10y2 + 3y5 + -1(14n2 + 4y3 + -12y5) = 0 8y + -10y2 + 3y5 + (14n2 * -1 + 4y3 * -1 + -12y5 * -1) = 0 8y + -10y2 + 3y5 + (-14n2 + -4y3 + 12y5) = 0 Reorder the terms: -14n2 + 8y + -10y2 + -4y3 + 3y5 + 12y5 = 0 Combine like terms: 3y5 + 12y5 = 15y5 -14n2 + 8y + -10y2 + -4y3 + 15y5 = 0 Solving -14n2 + 8y + -10y2 + -4y3 + 15y5 = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8y' to each side of the equation. -14n2 + 8y + -10y2 + -4y3 + -8y + 15y5 = 0 + -8y Reorder the terms: -14n2 + 8y + -8y + -10y2 + -4y3 + 15y5 = 0 + -8y Combine like terms: 8y + -8y = 0 -14n2 + 0 + -10y2 + -4y3 + 15y5 = 0 + -8y -14n2 + -10y2 + -4y3 + 15y5 = 0 + -8y Remove the zero: -14n2 + -10y2 + -4y3 + 15y5 = -8y Add '10y2' to each side of the equation. -14n2 + -10y2 + -4y3 + 10y2 + 15y5 = -8y + 10y2 Reorder the terms: -14n2 + -10y2 + 10y2 + -4y3 + 15y5 = -8y + 10y2 Combine like terms: -10y2 + 10y2 = 0 -14n2 + 0 + -4y3 + 15y5 = -8y + 10y2 -14n2 + -4y3 + 15y5 = -8y + 10y2 Add '4y3' to each side of the equation. -14n2 + -4y3 + 4y3 + 15y5 = -8y + 10y2 + 4y3 Combine like terms: -4y3 + 4y3 = 0 -14n2 + 0 + 15y5 = -8y + 10y2 + 4y3 -14n2 + 15y5 = -8y + 10y2 + 4y3 Add '-15y5' to each side of the equation. -14n2 + 15y5 + -15y5 = -8y + 10y2 + 4y3 + -15y5 Combine like terms: 15y5 + -15y5 = 0 -14n2 + 0 = -8y + 10y2 + 4y3 + -15y5 -14n2 = -8y + 10y2 + 4y3 + -15y5 Divide each side by '-14'. n2 = 0.5714285714y + -0.7142857143y2 + -0.2857142857y3 + 1.071428571y5 Simplifying n2 = 0.5714285714y + -0.7142857143y2 + -0.2857142857y3 + 1.071428571y5 Reorder the terms: n2 + -0.5714285714y + 0.7142857143y2 + 0.2857142857y3 + -1.071428571y5 = 0.5714285714y + -0.5714285714y + -0.7142857143y2 + 0.7142857143y2 + -0.2857142857y3 + 0.2857142857y3 + 1.071428571y5 + -1.071428571y5 Combine like terms: 0.5714285714y + -0.5714285714y = 0.0000000000 n2 + -0.5714285714y + 0.7142857143y2 + 0.2857142857y3 + -1.071428571y5 = 0.0000000000 + -0.7142857143y2 + 0.7142857143y2 + -0.2857142857y3 + 0.2857142857y3 + 1.071428571y5 + -1.071428571y5 n2 + -0.5714285714y + 0.7142857143y2 + 0.2857142857y3 + -1.071428571y5 = -0.7142857143y2 + 0.7142857143y2 + -0.2857142857y3 + 0.2857142857y3 + 1.071428571y5 + -1.071428571y5 Combine like terms: -0.7142857143y2 + 0.7142857143y2 = 0.0000000000 n2 + -0.5714285714y + 0.7142857143y2 + 0.2857142857y3 + -1.071428571y5 = 0.0000000000 + -0.2857142857y3 + 0.2857142857y3 + 1.071428571y5 + -1.071428571y5 n2 + -0.5714285714y + 0.7142857143y2 + 0.2857142857y3 + -1.071428571y5 = -0.2857142857y3 + 0.2857142857y3 + 1.071428571y5 + -1.071428571y5 Combine like terms: -0.2857142857y3 + 0.2857142857y3 = 0.0000000000 n2 + -0.5714285714y + 0.7142857143y2 + 0.2857142857y3 + -1.071428571y5 = 0.0000000000 + 1.071428571y5 + -1.071428571y5 n2 + -0.5714285714y + 0.7142857143y2 + 0.2857142857y3 + -1.071428571y5 = 1.071428571y5 + -1.071428571y5 Combine like terms: 1.071428571y5 + -1.071428571y5 = 0.000000000 n2 + -0.5714285714y + 0.7142857143y2 + 0.2857142857y3 + -1.071428571y5 = 0.000000000 The solution to this equation could not be determined.
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