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Simplifying (n + 3)(n + -10) = 0 Reorder the terms: (3 + n)(n + -10) = 0 Reorder the terms: (3 + n)(-10 + n) = 0 Multiply (3 + n) * (-10 + n) (3(-10 + n) + n(-10 + n)) = 0 ((-10 * 3 + n * 3) + n(-10 + n)) = 0 ((-30 + 3n) + n(-10 + n)) = 0 (-30 + 3n + (-10 * n + n * n)) = 0 (-30 + 3n + (-10n + n2)) = 0 Combine like terms: 3n + -10n = -7n (-30 + -7n + n2) = 0 Solving -30 + -7n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-3 + -1n)(10 + -1n) = 0Subproblem 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 '(10 + -1n)' equal to zero and attempt to solve: Simplifying 10 + -1n = 0 Solving 10 + -1n = 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 + -1n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1n = 0 + -10 -1n = 0 + -10 Combine like terms: 0 + -10 = -10 -1n = -10 Divide each side by '-1'. n = 10 Simplifying n = 10Solution
n = {-3, 10}
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