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Simplifying 12 + 6n + -4n(7 + -3n) = 6 + -7n 12 + 6n + (7 * -4n + -3n * -4n) = 6 + -7n 12 + 6n + (-28n + 12n2) = 6 + -7n Combine like terms: 6n + -28n = -22n 12 + -22n + 12n2 = 6 + -7n Solving 12 + -22n + 12n2 = 6 + -7n Solving for variable 'n'. Reorder the terms: 12 + -6 + -22n + 7n + 12n2 = 6 + -7n + -6 + 7n Combine like terms: 12 + -6 = 6 6 + -22n + 7n + 12n2 = 6 + -7n + -6 + 7n Combine like terms: -22n + 7n = -15n 6 + -15n + 12n2 = 6 + -7n + -6 + 7n Reorder the terms: 6 + -15n + 12n2 = 6 + -6 + -7n + 7n Combine like terms: 6 + -6 = 0 6 + -15n + 12n2 = 0 + -7n + 7n 6 + -15n + 12n2 = -7n + 7n Combine like terms: -7n + 7n = 0 6 + -15n + 12n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -5n + 4n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -5n + 4n2)' equal to zero and attempt to solve: Simplifying 2 + -5n + 4n2 = 0 Solving 2 + -5n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -1.25n + n2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.25n + -0.5 + n2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.25n + n2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.25n + n2 = 0 + -0.5 -1.25n + n2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.25n + n2 = -0.5 The n term is -1.25n. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25n + 0.390625 + n2 = -0.5 + 0.390625 Reorder the terms: 0.390625 + -1.25n + n2 = -0.5 + 0.390625 Combine like terms: -0.5 + 0.390625 = -0.109375 0.390625 + -1.25n + n2 = -0.109375 Factor a perfect square on the left side: (n + -0.625)(n + -0.625) = -0.109375 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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