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Simplifying 7n2 + 32n = 60 Reorder the terms: 32n + 7n2 = 60 Solving 32n + 7n2 = 60 Solving for variable 'n'. Reorder the terms: -60 + 32n + 7n2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 32n + 7n2 = 0 Factor a trinomial. (-6 + -1n)(10 + -7n) = 0Subproblem 1
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 = -6Subproblem 2
Set the factor '(10 + -7n)' equal to zero and attempt to solve: Simplifying 10 + -7n = 0 Solving 10 + -7n = 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 + -7n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7n = 0 + -10 -7n = 0 + -10 Combine like terms: 0 + -10 = -10 -7n = -10 Divide each side by '-7'. n = 1.428571429 Simplifying n = 1.428571429Solution
n = {-6, 1.428571429}
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