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Simplifying 8n2 + -56n + -243 = -3 Reorder the terms: -243 + -56n + 8n2 = -3 Solving -243 + -56n + 8n2 = -3 Solving for variable 'n'. Reorder the terms: -243 + 3 + -56n + 8n2 = -3 + 3 Combine like terms: -243 + 3 = -240 -240 + -56n + 8n2 = -3 + 3 Combine like terms: -3 + 3 = 0 -240 + -56n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-30 + -7n + n2) = 0 Factor a trinomial. 8((-3 + -1n)(10 + -1n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 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 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve: Simplifying 10 + -1n = 0 Solving 10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1n = 0 + -10 -1n = 0 + -10 Combine like terms: 0 + -10 = -10 -1n = -10 Divide each side by '-1'. n = 10 Simplifying n = 10Solution
n = {-3, 10}
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