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Simplifying (8r + -3)(r + 2) = 0 Reorder the terms: (-3 + 8r)(r + 2) = 0 Reorder the terms: (-3 + 8r)(2 + r) = 0 Multiply (-3 + 8r) * (2 + r) (-3(2 + r) + 8r * (2 + r)) = 0 ((2 * -3 + r * -3) + 8r * (2 + r)) = 0 ((-6 + -3r) + 8r * (2 + r)) = 0 (-6 + -3r + (2 * 8r + r * 8r)) = 0 (-6 + -3r + (16r + 8r2)) = 0 Combine like terms: -3r + 16r = 13r (-6 + 13r + 8r2) = 0 Solving -6 + 13r + 8r2 = 0 Solving for variable 'r'. Factor a trinomial. (-2 + -1r)(3 + -8r) = 0Subproblem 1
Set the factor '(-2 + -1r)' equal to zero and attempt to solve: Simplifying -2 + -1r = 0 Solving -2 + -1r = 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 + -1r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1r = 0 + 2 -1r = 0 + 2 Combine like terms: 0 + 2 = 2 -1r = 2 Divide each side by '-1'. r = -2 Simplifying r = -2Subproblem 2
Set the factor '(3 + -8r)' equal to zero and attempt to solve: Simplifying 3 + -8r = 0 Solving 3 + -8r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8r = 0 + -3 -8r = 0 + -3 Combine like terms: 0 + -3 = -3 -8r = -3 Divide each side by '-8'. r = 0.375 Simplifying r = 0.375Solution
r = {-2, 0.375}
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