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Simplifying 24n + 30n2 = 5n + 4 Reorder the terms: 24n + 30n2 = 4 + 5n Solving 24n + 30n2 = 4 + 5n Solving for variable 'n'. Reorder the terms: -4 + 24n + -5n + 30n2 = 4 + 5n + -4 + -5n Combine like terms: 24n + -5n = 19n -4 + 19n + 30n2 = 4 + 5n + -4 + -5n Reorder the terms: -4 + 19n + 30n2 = 4 + -4 + 5n + -5n Combine like terms: 4 + -4 = 0 -4 + 19n + 30n2 = 0 + 5n + -5n -4 + 19n + 30n2 = 5n + -5n Combine like terms: 5n + -5n = 0 -4 + 19n + 30n2 = 0 Factor a trinomial. (-4 + -5n)(1 + -6n) = 0Subproblem 1
Set the factor '(-4 + -5n)' equal to zero and attempt to solve: Simplifying -4 + -5n = 0 Solving -4 + -5n = 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 + -5n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5n = 0 + 4 -5n = 0 + 4 Combine like terms: 0 + 4 = 4 -5n = 4 Divide each side by '-5'. n = -0.8 Simplifying n = -0.8Subproblem 2
Set the factor '(1 + -6n)' equal to zero and attempt to solve: Simplifying 1 + -6n = 0 Solving 1 + -6n = 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 + -6n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6n = 0 + -1 -6n = 0 + -1 Combine like terms: 0 + -1 = -1 -6n = -1 Divide each side by '-6'. n = 0.1666666667 Simplifying n = 0.1666666667Solution
n = {-0.8, 0.1666666667}
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