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Simplifying (4n + 9)(n + -6) = 0 Reorder the terms: (9 + 4n)(n + -6) = 0 Reorder the terms: (9 + 4n)(-6 + n) = 0 Multiply (9 + 4n) * (-6 + n) (9(-6 + n) + 4n * (-6 + n)) = 0 ((-6 * 9 + n * 9) + 4n * (-6 + n)) = 0 ((-54 + 9n) + 4n * (-6 + n)) = 0 (-54 + 9n + (-6 * 4n + n * 4n)) = 0 (-54 + 9n + (-24n + 4n2)) = 0 Combine like terms: 9n + -24n = -15n (-54 + -15n + 4n2) = 0 Solving -54 + -15n + 4n2 = 0 Solving for variable 'n'. Factor a trinomial. (-9 + -4n)(6 + -1n) = 0Subproblem 1
Set the factor '(-9 + -4n)' equal to zero and attempt to solve: Simplifying -9 + -4n = 0 Solving -9 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4n = 0 + 9 -4n = 0 + 9 Combine like terms: 0 + 9 = 9 -4n = 9 Divide each side by '-4'. n = -2.25 Simplifying n = -2.25Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-2.25, 6}
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