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Simplifying (3r + 2)(r + -5) = 0 Reorder the terms: (2 + 3r)(r + -5) = 0 Reorder the terms: (2 + 3r)(-5 + r) = 0 Multiply (2 + 3r) * (-5 + r) (2(-5 + r) + 3r * (-5 + r)) = 0 ((-5 * 2 + r * 2) + 3r * (-5 + r)) = 0 ((-10 + 2r) + 3r * (-5 + r)) = 0 (-10 + 2r + (-5 * 3r + r * 3r)) = 0 (-10 + 2r + (-15r + 3r2)) = 0 Combine like terms: 2r + -15r = -13r (-10 + -13r + 3r2) = 0 Solving -10 + -13r + 3r2 = 0 Solving for variable 'r'. Factor a trinomial. (-2 + -3r)(5 + -1r) = 0Subproblem 1
Set the factor '(-2 + -3r)' equal to zero and attempt to solve: Simplifying -2 + -3r = 0 Solving -2 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3r = 0 + 2 -3r = 0 + 2 Combine like terms: 0 + 2 = 2 -3r = 2 Divide each side by '-3'. r = -0.6666666667 Simplifying r = -0.6666666667Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5Solution
r = {-0.6666666667, 5}
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