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Simplifying (r + 5)(r + -6) = 0 Reorder the terms: (5 + r)(r + -6) = 0 Reorder the terms: (5 + r)(-6 + r) = 0 Multiply (5 + r) * (-6 + r) (5(-6 + r) + r(-6 + r)) = 0 ((-6 * 5 + r * 5) + r(-6 + r)) = 0 ((-30 + 5r) + r(-6 + r)) = 0 (-30 + 5r + (-6 * r + r * r)) = 0 (-30 + 5r + (-6r + r2)) = 0 Combine like terms: 5r + -6r = -1r (-30 + -1r + r2) = 0 Solving -30 + -1r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (-5 + -1r)(6 + -1r) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve: Simplifying 6 + -1r = 0 Solving 6 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1r = 0 + -6 -1r = 0 + -6 Combine like terms: 0 + -6 = -6 -1r = -6 Divide each side by '-1'. r = 6 Simplifying r = 6Solution
r = {-5, 6}
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