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Simplifying (9r + 4)(5r + -15) = 0 Reorder the terms: (4 + 9r)(5r + -15) = 0 Reorder the terms: (4 + 9r)(-15 + 5r) = 0 Multiply (4 + 9r) * (-15 + 5r) (4(-15 + 5r) + 9r * (-15 + 5r)) = 0 ((-15 * 4 + 5r * 4) + 9r * (-15 + 5r)) = 0 ((-60 + 20r) + 9r * (-15 + 5r)) = 0 (-60 + 20r + (-15 * 9r + 5r * 9r)) = 0 (-60 + 20r + (-135r + 45r2)) = 0 Combine like terms: 20r + -135r = -115r (-60 + -115r + 45r2) = 0 Solving -60 + -115r + 45r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5'. 5(-12 + -23r + 9r2) = 0 Factor a trinomial. 5((-4 + -9r)(3 + -1r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + -9r)' equal to zero and attempt to solve: Simplifying -4 + -9r = 0 Solving -4 + -9r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -9r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -9r = 0 + 4 -9r = 0 + 4 Combine like terms: 0 + 4 = 4 -9r = 4 Divide each side by '-9'. r = -0.4444444444 Simplifying r = -0.4444444444Subproblem 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 = {-0.4444444444, 3}
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