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Simplifying (2r + -5)(r + 2) = 0 Reorder the terms: (-5 + 2r)(r + 2) = 0 Reorder the terms: (-5 + 2r)(2 + r) = 0 Multiply (-5 + 2r) * (2 + r) (-5(2 + r) + 2r * (2 + r)) = 0 ((2 * -5 + r * -5) + 2r * (2 + r)) = 0 ((-10 + -5r) + 2r * (2 + r)) = 0 (-10 + -5r + (2 * 2r + r * 2r)) = 0 (-10 + -5r + (4r + 2r2)) = 0 Combine like terms: -5r + 4r = -1r (-10 + -1r + 2r2) = 0 Solving -10 + -1r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (-2 + -1r)(5 + -2r) = 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 '(5 + -2r)' equal to zero and attempt to solve: Simplifying 5 + -2r = 0 Solving 5 + -2r = 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 + -2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2r = 0 + -5 -2r = 0 + -5 Combine like terms: 0 + -5 = -5 -2r = -5 Divide each side by '-2'. r = 2.5 Simplifying r = 2.5Solution
r = {-2, 2.5}
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