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Simplifying 7 + -2n = 8n(4n) Remove parenthesis around (4n) 7 + -2n = 8n * 4n Reorder the terms for easier multiplication: 7 + -2n = 8 * 4n * n Multiply 8 * 4 7 + -2n = 32n * n Multiply n * n 7 + -2n = 32n2 Solving 7 + -2n = 32n2 Solving for variable 'n'. Combine like terms: 32n2 + -32n2 = 0 7 + -2n + -32n2 = 0 Factor a trinomial. (7 + -16n)(1 + 2n) = 0Subproblem 1
Set the factor '(7 + -16n)' equal to zero and attempt to solve: Simplifying 7 + -16n = 0 Solving 7 + -16n = 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 + -16n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -16n = 0 + -7 -16n = 0 + -7 Combine like terms: 0 + -7 = -7 -16n = -7 Divide each side by '-16'. n = 0.4375 Simplifying n = 0.4375Subproblem 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 = {0.4375, -0.5}
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