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Simplifying N(x) = x(480 + -6x) Multiply N * x xN = x(480 + -6x) xN = (480 * x + -6x * x) xN = (480x + -6x2) Solving xN = 480x + -6x2 Solving for variable 'x'. Reorder the terms: -480x + xN + 6x2 = 480x + -6x2 + -480x + 6x2 Reorder the terms: -480x + xN + 6x2 = 480x + -480x + -6x2 + 6x2 Combine like terms: 480x + -480x = 0 -480x + xN + 6x2 = 0 + -6x2 + 6x2 -480x + xN + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -480x + xN + 6x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-480 + N + 6x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-480 + N + 6x)' equal to zero and attempt to solve: Simplifying -480 + N + 6x = 0 Solving -480 + N + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '480' to each side of the equation. -480 + N + 480 + 6x = 0 + 480 Reorder the terms: -480 + 480 + N + 6x = 0 + 480 Combine like terms: -480 + 480 = 0 0 + N + 6x = 0 + 480 N + 6x = 0 + 480 Combine like terms: 0 + 480 = 480 N + 6x = 480 Add '-1N' to each side of the equation. N + -1N + 6x = 480 + -1N Combine like terms: N + -1N = 0 0 + 6x = 480 + -1N 6x = 480 + -1N Divide each side by '6'. x = 80 + -0.1666666667N Simplifying x = 80 + -0.1666666667NSolution
x = {0, 80 + -0.1666666667N}
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