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Simplifying (5r + 3)(2r + -6) = 0 Reorder the terms: (3 + 5r)(2r + -6) = 0 Reorder the terms: (3 + 5r)(-6 + 2r) = 0 Multiply (3 + 5r) * (-6 + 2r) (3(-6 + 2r) + 5r * (-6 + 2r)) = 0 ((-6 * 3 + 2r * 3) + 5r * (-6 + 2r)) = 0 ((-18 + 6r) + 5r * (-6 + 2r)) = 0 (-18 + 6r + (-6 * 5r + 2r * 5r)) = 0 (-18 + 6r + (-30r + 10r2)) = 0 Combine like terms: 6r + -30r = -24r (-18 + -24r + 10r2) = 0 Solving -18 + -24r + 10r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -12r + 5r2) = 0 Factor a trinomial. 2((-3 + -5r)(3 + -1r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -5r)' equal to zero and attempt to solve: Simplifying -3 + -5r = 0 Solving -3 + -5r = 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 + -5r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5r = 0 + 3 -5r = 0 + 3 Combine like terms: 0 + 3 = 3 -5r = 3 Divide each side by '-5'. r = -0.6 Simplifying r = -0.6Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 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 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {-0.6, 3}
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