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Simplifying (2n + -3)(3n + -10) = 0 Reorder the terms: (-3 + 2n)(3n + -10) = 0 Reorder the terms: (-3 + 2n)(-10 + 3n) = 0 Multiply (-3 + 2n) * (-10 + 3n) (-3(-10 + 3n) + 2n * (-10 + 3n)) = 0 ((-10 * -3 + 3n * -3) + 2n * (-10 + 3n)) = 0 ((30 + -9n) + 2n * (-10 + 3n)) = 0 (30 + -9n + (-10 * 2n + 3n * 2n)) = 0 (30 + -9n + (-20n + 6n2)) = 0 Combine like terms: -9n + -20n = -29n (30 + -29n + 6n2) = 0 Solving 30 + -29n + 6n2 = 0 Solving for variable 'n'. Factor a trinomial. (3 + -2n)(10 + -3n) = 0Subproblem 1
Set the factor '(3 + -2n)' equal to zero and attempt to solve: Simplifying 3 + -2n = 0 Solving 3 + -2n = 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 + -2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2n = 0 + -3 -2n = 0 + -3 Combine like terms: 0 + -3 = -3 -2n = -3 Divide each side by '-2'. n = 1.5 Simplifying n = 1.5Subproblem 2
Set the factor '(10 + -3n)' equal to zero and attempt to solve: Simplifying 10 + -3n = 0 Solving 10 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3n = 0 + -10 -3n = 0 + -10 Combine like terms: 0 + -10 = -10 -3n = -10 Divide each side by '-3'. n = 3.333333333 Simplifying n = 3.333333333Solution
n = {1.5, 3.333333333}
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