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Simplifying n(-3 + 7n) = 972 (-3 * n + 7n * n) = 972 (-3n + 7n2) = 972 Solving -3n + 7n2 = 972 Solving for variable 'n'. Reorder the terms: -972 + -3n + 7n2 = 972 + -972 Combine like terms: 972 + -972 = 0 -972 + -3n + 7n2 = 0 Factor a trinomial. (-81 + -7n)(12 + -1n) = 0Subproblem 1
Set the factor '(-81 + -7n)' equal to zero and attempt to solve: Simplifying -81 + -7n = 0 Solving -81 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '81' to each side of the equation. -81 + 81 + -7n = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -7n = 0 + 81 -7n = 0 + 81 Combine like terms: 0 + 81 = 81 -7n = 81 Divide each side by '-7'. n = -11.57142857 Simplifying n = -11.57142857Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve: Simplifying 12 + -1n = 0 Solving 12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1n = 0 + -12 -1n = 0 + -12 Combine like terms: 0 + -12 = -12 -1n = -12 Divide each side by '-1'. n = 12 Simplifying n = 12Solution
n = {-11.57142857, 12}
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