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Simplifying n2(7n + -5) * 3(7n + -5) = 0 Reorder the terms: n2(-5 + 7n) * 3(7n + -5) = 0 Reorder the terms: n2(-5 + 7n) * 3(-5 + 7n) = 0 Reorder the terms for easier multiplication: 3n2(-5 + 7n)(-5 + 7n) = 0 Multiply (-5 + 7n) * (-5 + 7n) 3n2(-5(-5 + 7n) + 7n * (-5 + 7n)) = 0 3n2((-5 * -5 + 7n * -5) + 7n * (-5 + 7n)) = 0 3n2((25 + -35n) + 7n * (-5 + 7n)) = 0 3n2(25 + -35n + (-5 * 7n + 7n * 7n)) = 0 3n2(25 + -35n + (-35n + 49n2)) = 0 Combine like terms: -35n + -35n = -70n 3n2(25 + -70n + 49n2) = 0 (25 * 3n2 + -70n * 3n2 + 49n2 * 3n2) = 0 (75n2 + -210n3 + 147n4) = 0 Solving 75n2 + -210n3 + 147n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n2'. 3n2(25 + -70n + 49n2) = 0 Factor a trinomial. 3n2((5 + -7n)(5 + -7n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}Subproblem 2
Set the factor '(5 + -7n)' equal to zero and attempt to solve: Simplifying 5 + -7n = 0 Solving 5 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7n = 0 + -5 -7n = 0 + -5 Combine like terms: 0 + -5 = -5 -7n = -5 Divide each side by '-7'. n = 0.7142857143 Simplifying n = 0.7142857143Subproblem 3
Set the factor '(5 + -7n)' equal to zero and attempt to solve: Simplifying 5 + -7n = 0 Solving 5 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7n = 0 + -5 -7n = 0 + -5 Combine like terms: 0 + -5 = -5 -7n = -5 Divide each side by '-7'. n = 0.7142857143 Simplifying n = 0.7142857143Solution
n = {0, 0.7142857143, 0.7142857143}
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