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Simplifying 32n2 + 25n + -10 = -3n2 Reorder the terms: -10 + 25n + 32n2 = -3n2 Solving -10 + 25n + 32n2 = -3n2 Solving for variable 'n'. Combine like terms: 32n2 + 3n2 = 35n2 -10 + 25n + 35n2 = -3n2 + 3n2 Combine like terms: -3n2 + 3n2 = 0 -10 + 25n + 35n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 5n + 7n2) = 0 Factor a trinomial. 5((-1 + -1n)(2 + -7n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -1n)' equal to zero and attempt to solve: Simplifying -1 + -1n = 0 Solving -1 + -1n = 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 + -1n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1n = 0 + 1 -1n = 0 + 1 Combine like terms: 0 + 1 = 1 -1n = 1 Divide each side by '-1'. n = -1 Simplifying n = -1Subproblem 2
Set the factor '(2 + -7n)' equal to zero and attempt to solve: Simplifying 2 + -7n = 0 Solving 2 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7n = 0 + -2 -7n = 0 + -2 Combine like terms: 0 + -2 = -2 -7n = -2 Divide each side by '-7'. n = 0.2857142857 Simplifying n = 0.2857142857Solution
n = {-1, 0.2857142857}
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