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Simplifying 4n4 + -4n3 = 48n2 Reorder the terms: -4n3 + 4n4 = 48n2 Solving -4n3 + 4n4 = 48n2 Solving for variable 'n'. Reorder the terms: -48n2 + -4n3 + 4n4 = 48n2 + -48n2 Combine like terms: 48n2 + -48n2 = 0 -48n2 + -4n3 + 4n4 = 0 Factor out the Greatest Common Factor (GCF), '4n2'. 4n2(-12 + -1n + n2) = 0 Factor a trinomial. 4n2((-3 + -1n)(4 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}Subproblem 2
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 3
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {0, -3, 4}
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