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Simplifying 9r2 + 20r + -20 = 2r2 + -3r Reorder the terms: -20 + 20r + 9r2 = 2r2 + -3r Reorder the terms: -20 + 20r + 9r2 = -3r + 2r2 Solving -20 + 20r + 9r2 = -3r + 2r2 Solving for variable 'r'. Reorder the terms: -20 + 20r + 3r + 9r2 + -2r2 = -3r + 2r2 + 3r + -2r2 Combine like terms: 20r + 3r = 23r -20 + 23r + 9r2 + -2r2 = -3r + 2r2 + 3r + -2r2 Combine like terms: 9r2 + -2r2 = 7r2 -20 + 23r + 7r2 = -3r + 2r2 + 3r + -2r2 Reorder the terms: -20 + 23r + 7r2 = -3r + 3r + 2r2 + -2r2 Combine like terms: -3r + 3r = 0 -20 + 23r + 7r2 = 0 + 2r2 + -2r2 -20 + 23r + 7r2 = 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 -20 + 23r + 7r2 = 0 Factor a trinomial. (-4 + -1r)(5 + -7r) = 0Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 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 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4Subproblem 2
Set the factor '(5 + -7r)' equal to zero and attempt to solve: Simplifying 5 + -7r = 0 Solving 5 + -7r = 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 + -7r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7r = 0 + -5 -7r = 0 + -5 Combine like terms: 0 + -5 = -5 -7r = -5 Divide each side by '-7'. r = 0.7142857143 Simplifying r = 0.7142857143Solution
r = {-4, 0.7142857143}
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