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Simplifying 4n2 + 19n + 7 = -6n2 Reorder the terms: 7 + 19n + 4n2 = -6n2 Solving 7 + 19n + 4n2 = -6n2 Solving for variable 'n'. Combine like terms: 4n2 + 6n2 = 10n2 7 + 19n + 10n2 = -6n2 + 6n2 Combine like terms: -6n2 + 6n2 = 0 7 + 19n + 10n2 = 0 Factor a trinomial. (7 + 5n)(1 + 2n) = 0Subproblem 1
Set the factor '(7 + 5n)' equal to zero and attempt to solve: Simplifying 7 + 5n = 0 Solving 7 + 5n = 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 + 5n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5n = 0 + -7 5n = 0 + -7 Combine like terms: 0 + -7 = -7 5n = -7 Divide each side by '5'. n = -1.4 Simplifying n = -1.4Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Solution
n = {-1.4, -0.5}
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