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Simplifying (7n + -2)(5n + 15) = 0 Reorder the terms: (-2 + 7n)(5n + 15) = 0 Reorder the terms: (-2 + 7n)(15 + 5n) = 0 Multiply (-2 + 7n) * (15 + 5n) (-2(15 + 5n) + 7n * (15 + 5n)) = 0 ((15 * -2 + 5n * -2) + 7n * (15 + 5n)) = 0 ((-30 + -10n) + 7n * (15 + 5n)) = 0 (-30 + -10n + (15 * 7n + 5n * 7n)) = 0 (-30 + -10n + (105n + 35n2)) = 0 Combine like terms: -10n + 105n = 95n (-30 + 95n + 35n2) = 0 Solving -30 + 95n + 35n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + 19n + 7n2) = 0 Factor a trinomial. 5((-3 + -1n)(2 + -7n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 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 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
Set the factor '(2 + -7n)' equal to zero and attempt to solve: Simplifying 2 + -7n = 0 Solving 2 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7n = 0 + -2 -7n = 0 + -2 Combine like terms: 0 + -2 = -2 -7n = -2 Divide each side by '-7'. n = 0.2857142857 Simplifying n = 0.2857142857Solution
n = {-3, 0.2857142857}
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