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Simplifying 7(n + -4)(6 + -2n) = 8n Reorder the terms: 7(-4 + n)(6 + -2n) = 8n Multiply (-4 + n) * (6 + -2n) 7(-4(6 + -2n) + n(6 + -2n)) = 8n 7((6 * -4 + -2n * -4) + n(6 + -2n)) = 8n 7((-24 + 8n) + n(6 + -2n)) = 8n 7(-24 + 8n + (6 * n + -2n * n)) = 8n 7(-24 + 8n + (6n + -2n2)) = 8n Combine like terms: 8n + 6n = 14n 7(-24 + 14n + -2n2) = 8n (-24 * 7 + 14n * 7 + -2n2 * 7) = 8n (-168 + 98n + -14n2) = 8n Solving -168 + 98n + -14n2 = 8n Solving for variable 'n'. Reorder the terms: -168 + 98n + -8n + -14n2 = 8n + -8n Combine like terms: 98n + -8n = 90n -168 + 90n + -14n2 = 8n + -8n Combine like terms: 8n + -8n = 0 -168 + 90n + -14n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-84 + 45n + -7n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-84 + 45n + -7n2)' equal to zero and attempt to solve: Simplifying -84 + 45n + -7n2 = 0 Solving -84 + 45n + -7n2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 12 + -6.428571429n + n2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -6.428571429n + -12 + n2 = 0 + -12 Reorder the terms: 12 + -12 + -6.428571429n + n2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -6.428571429n + n2 = 0 + -12 -6.428571429n + n2 = 0 + -12 Combine like terms: 0 + -12 = -12 -6.428571429n + n2 = -12 The n term is -6.428571429n. Take half its coefficient (-3.214285715). Square it (10.33163266) and add it to both sides. Add '10.33163266' to each side of the equation. -6.428571429n + 10.33163266 + n2 = -12 + 10.33163266 Reorder the terms: 10.33163266 + -6.428571429n + n2 = -12 + 10.33163266 Combine like terms: -12 + 10.33163266 = -1.66836734 10.33163266 + -6.428571429n + n2 = -1.66836734 Factor a perfect square on the left side: (n + -3.214285715)(n + -3.214285715) = -1.66836734 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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