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Simplifying (7n + -5)(3n + -5) = 0 Reorder the terms: (-5 + 7n)(3n + -5) = 0 Reorder the terms: (-5 + 7n)(-5 + 3n) = 0 Multiply (-5 + 7n) * (-5 + 3n) (-5(-5 + 3n) + 7n * (-5 + 3n)) = 0 ((-5 * -5 + 3n * -5) + 7n * (-5 + 3n)) = 0 ((25 + -15n) + 7n * (-5 + 3n)) = 0 (25 + -15n + (-5 * 7n + 3n * 7n)) = 0 (25 + -15n + (-35n + 21n2)) = 0 Combine like terms: -15n + -35n = -50n (25 + -50n + 21n2) = 0 Solving 25 + -50n + 21n2 = 0 Solving for variable 'n'. Factor a trinomial. (5 + -7n)(5 + -3n) = 0Subproblem 1
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 2
Set the factor '(5 + -3n)' equal to zero and attempt to solve: Simplifying 5 + -3n = 0 Solving 5 + -3n = 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 + -3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n = 0 + -5 -3n = 0 + -5 Combine like terms: 0 + -5 = -5 -3n = -5 Divide each side by '-3'. n = 1.666666667 Simplifying n = 1.666666667Solution
n = {0.7142857143, 1.666666667}
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