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Simplifying (r + -5)(r + 3) + (r + -5)(r + 8) = 0 Reorder the terms: (-5 + r)(r + 3) + (r + -5)(r + 8) = 0 Reorder the terms: (-5 + r)(3 + r) + (r + -5)(r + 8) = 0 Multiply (-5 + r) * (3 + r) (-5(3 + r) + r(3 + r)) + (r + -5)(r + 8) = 0 ((3 * -5 + r * -5) + r(3 + r)) + (r + -5)(r + 8) = 0 ((-15 + -5r) + r(3 + r)) + (r + -5)(r + 8) = 0 (-15 + -5r + (3 * r + r * r)) + (r + -5)(r + 8) = 0 (-15 + -5r + (3r + r2)) + (r + -5)(r + 8) = 0 Combine like terms: -5r + 3r = -2r (-15 + -2r + r2) + (r + -5)(r + 8) = 0 Reorder the terms: -15 + -2r + r2 + (-5 + r)(r + 8) = 0 Reorder the terms: -15 + -2r + r2 + (-5 + r)(8 + r) = 0 Multiply (-5 + r) * (8 + r) -15 + -2r + r2 + (-5(8 + r) + r(8 + r)) = 0 -15 + -2r + r2 + ((8 * -5 + r * -5) + r(8 + r)) = 0 -15 + -2r + r2 + ((-40 + -5r) + r(8 + r)) = 0 -15 + -2r + r2 + (-40 + -5r + (8 * r + r * r)) = 0 -15 + -2r + r2 + (-40 + -5r + (8r + r2)) = 0 Combine like terms: -5r + 8r = 3r -15 + -2r + r2 + (-40 + 3r + r2) = 0 Reorder the terms: -15 + -40 + -2r + 3r + r2 + r2 = 0 Combine like terms: -15 + -40 = -55 -55 + -2r + 3r + r2 + r2 = 0 Combine like terms: -2r + 3r = 1r -55 + 1r + r2 + r2 = 0 Combine like terms: r2 + r2 = 2r2 -55 + 1r + 2r2 = 0 Solving -55 + 1r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (-11 + -2r)(5 + -1r) = 0Subproblem 1
Set the factor '(-11 + -2r)' equal to zero and attempt to solve: Simplifying -11 + -2r = 0 Solving -11 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -2r = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2r = 0 + 11 -2r = 0 + 11 Combine like terms: 0 + 11 = 11 -2r = 11 Divide each side by '-2'. r = -5.5 Simplifying r = -5.5Subproblem 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 = {-5.5, 5}
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