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Simplifying 27n2 + -12 = (3n + 3)(9n + -4) Reorder the terms: -12 + 27n2 = (3n + 3)(9n + -4) Reorder the terms: -12 + 27n2 = (3 + 3n)(9n + -4) Reorder the terms: -12 + 27n2 = (3 + 3n)(-4 + 9n) Multiply (3 + 3n) * (-4 + 9n) -12 + 27n2 = (3(-4 + 9n) + 3n * (-4 + 9n)) -12 + 27n2 = ((-4 * 3 + 9n * 3) + 3n * (-4 + 9n)) -12 + 27n2 = ((-12 + 27n) + 3n * (-4 + 9n)) -12 + 27n2 = (-12 + 27n + (-4 * 3n + 9n * 3n)) -12 + 27n2 = (-12 + 27n + (-12n + 27n2)) Combine like terms: 27n + -12n = 15n -12 + 27n2 = (-12 + 15n + 27n2) Add '12' to each side of the equation. -12 + 12 + 27n2 = -12 + 15n + 12 + 27n2 Combine like terms: -12 + 12 = 0 0 + 27n2 = -12 + 15n + 12 + 27n2 27n2 = -12 + 15n + 12 + 27n2 Reorder the terms: 27n2 = -12 + 12 + 15n + 27n2 Combine like terms: -12 + 12 = 0 27n2 = 0 + 15n + 27n2 27n2 = 15n + 27n2 Add '-27n2' to each side of the equation. 27n2 + -27n2 = 15n + 27n2 + -27n2 Combine like terms: 27n2 + -27n2 = 0 0 = 15n + 27n2 + -27n2 Combine like terms: 27n2 + -27n2 = 0 0 = 15n + 0 0 = 15n Solving 0 = 15n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15n' to each side of the equation. 0 + -15n = 15n + -15n Remove the zero: -15n = 15n + -15n Combine like terms: 15n + -15n = 0 -15n = 0 Divide each side by '-15'. n = 0 Simplifying n = 0
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