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Simplifying 7n2 = 53n + -28 Reorder the terms: 7n2 = -28 + 53n Solving 7n2 = -28 + 53n Solving for variable 'n'. Reorder the terms: 28 + -53n + 7n2 = -28 + 53n + 28 + -53n Reorder the terms: 28 + -53n + 7n2 = -28 + 28 + 53n + -53n Combine like terms: -28 + 28 = 0 28 + -53n + 7n2 = 0 + 53n + -53n 28 + -53n + 7n2 = 53n + -53n Combine like terms: 53n + -53n = 0 28 + -53n + 7n2 = 0 Factor a trinomial. (4 + -7n)(7 + -1n) = 0Subproblem 1
Set the factor '(4 + -7n)' equal to zero and attempt to solve: Simplifying 4 + -7n = 0 Solving 4 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7n = 0 + -4 -7n = 0 + -4 Combine like terms: 0 + -4 = -4 -7n = -4 Divide each side by '-7'. n = 0.5714285714 Simplifying n = 0.5714285714Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {0.5714285714, 7}
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