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Simplifying (-5r + -3)(-4r + 5) = 0 Reorder the terms: (-3 + -5r)(-4r + 5) = 0 Reorder the terms: (-3 + -5r)(5 + -4r) = 0 Multiply (-3 + -5r) * (5 + -4r) (-3(5 + -4r) + -5r * (5 + -4r)) = 0 ((5 * -3 + -4r * -3) + -5r * (5 + -4r)) = 0 ((-15 + 12r) + -5r * (5 + -4r)) = 0 (-15 + 12r + (5 * -5r + -4r * -5r)) = 0 (-15 + 12r + (-25r + 20r2)) = 0 Combine like terms: 12r + -25r = -13r (-15 + -13r + 20r2) = 0 Solving -15 + -13r + 20r2 = 0 Solving for variable 'r'. Factor a trinomial. (-3 + -5r)(5 + -4r) = 0Subproblem 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 '(5 + -4r)' equal to zero and attempt to solve: Simplifying 5 + -4r = 0 Solving 5 + -4r = 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 + -4r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4r = 0 + -5 -4r = 0 + -5 Combine like terms: 0 + -5 = -5 -4r = -5 Divide each side by '-4'. r = 1.25 Simplifying r = 1.25Solution
r = {-0.6, 1.25}
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