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Simplifying 7n2 = 46n + 21 Reorder the terms: 7n2 = 21 + 46n Solving 7n2 = 21 + 46n Solving for variable 'n'. Reorder the terms: -21 + -46n + 7n2 = 21 + 46n + -21 + -46n Reorder the terms: -21 + -46n + 7n2 = 21 + -21 + 46n + -46n Combine like terms: 21 + -21 = 0 -21 + -46n + 7n2 = 0 + 46n + -46n -21 + -46n + 7n2 = 46n + -46n Combine like terms: 46n + -46n = 0 -21 + -46n + 7n2 = 0 Factor a trinomial. (-3 + -7n)(7 + -1n) = 0Subproblem 1
Set the factor '(-3 + -7n)' equal to zero and attempt to solve: Simplifying -3 + -7n = 0 Solving -3 + -7n = 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 + -7n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7n = 0 + 3 -7n = 0 + 3 Combine like terms: 0 + 3 = 3 -7n = 3 Divide each side by '-7'. n = -0.4285714286 Simplifying n = -0.4285714286Subproblem 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 = {-0.4285714286, 7}
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