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Simplifying (r + -2)(4r + -9) = 0 Reorder the terms: (-2 + r)(4r + -9) = 0 Reorder the terms: (-2 + r)(-9 + 4r) = 0 Multiply (-2 + r) * (-9 + 4r) (-2(-9 + 4r) + r(-9 + 4r)) = 0 ((-9 * -2 + 4r * -2) + r(-9 + 4r)) = 0 ((18 + -8r) + r(-9 + 4r)) = 0 (18 + -8r + (-9 * r + 4r * r)) = 0 (18 + -8r + (-9r + 4r2)) = 0 Combine like terms: -8r + -9r = -17r (18 + -17r + 4r2) = 0 Solving 18 + -17r + 4r2 = 0 Solving for variable 'r'. Factor a trinomial. (2 + -1r)(9 + -4r) = 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 '(9 + -4r)' equal to zero and attempt to solve: Simplifying 9 + -4r = 0 Solving 9 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4r = 0 + -9 -4r = 0 + -9 Combine like terms: 0 + -9 = -9 -4r = -9 Divide each side by '-4'. r = 2.25 Simplifying r = 2.25Solution
r = {2, 2.25}
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