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Simplifying (4n + -2)(4n + -2) = 0 Reorder the terms: (-2 + 4n)(4n + -2) = 0 Reorder the terms: (-2 + 4n)(-2 + 4n) = 0 Multiply (-2 + 4n) * (-2 + 4n) (-2(-2 + 4n) + 4n * (-2 + 4n)) = 0 ((-2 * -2 + 4n * -2) + 4n * (-2 + 4n)) = 0 ((4 + -8n) + 4n * (-2 + 4n)) = 0 (4 + -8n + (-2 * 4n + 4n * 4n)) = 0 (4 + -8n + (-8n + 16n2)) = 0 Combine like terms: -8n + -8n = -16n (4 + -16n + 16n2) = 0 Solving 4 + -16n + 16n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -4n + 4n2) = 0 Factor a trinomial. 4((1 + -2n)(1 + -2n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Solution
n = {0.5, 0.5}
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