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Simplifying 21n2 + 150n + -144 = 0 Reorder the terms: -144 + 150n + 21n2 = 0 Solving -144 + 150n + 21n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-48 + 50n + 7n2) = 0 Factor a trinomial. 3((-8 + -1n)(6 + -7n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8Subproblem 2
Set the factor '(6 + -7n)' equal to zero and attempt to solve: Simplifying 6 + -7n = 0 Solving 6 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7n = 0 + -6 -7n = 0 + -6 Combine like terms: 0 + -6 = -6 -7n = -6 Divide each side by '-7'. n = 0.8571428571 Simplifying n = 0.8571428571Solution
n = {-8, 0.8571428571}
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