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Simplifying -4n(n + -4) + -23 = -7 Reorder the terms: -4n(-4 + n) + -23 = -7 (-4 * -4n + n * -4n) + -23 = -7 (16n + -4n2) + -23 = -7 Reorder the terms: -23 + 16n + -4n2 = -7 Solving -23 + 16n + -4n2 = -7 Solving for variable 'n'. Reorder the terms: -23 + 7 + 16n + -4n2 = -7 + 7 Combine like terms: -23 + 7 = -16 -16 + 16n + -4n2 = -7 + 7 Combine like terms: -7 + 7 = 0 -16 + 16n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 4n + -1n2) = 0 Factor a trinomial. 4((-2 + n)(2 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + n)' equal to zero and attempt to solve: Simplifying -2 + n = 0 Solving -2 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + n = 0 + 2 n = 0 + 2 Combine like terms: 0 + 2 = 2 n = 2 Simplifying n = 2Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Solution
n = {2, 2}
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