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Simplifying (r + 4)(r + -9) = 0 Reorder the terms: (4 + r)(r + -9) = 0 Reorder the terms: (4 + r)(-9 + r) = 0 Multiply (4 + r) * (-9 + r) (4(-9 + r) + r(-9 + r)) = 0 ((-9 * 4 + r * 4) + r(-9 + r)) = 0 ((-36 + 4r) + r(-9 + r)) = 0 (-36 + 4r + (-9 * r + r * r)) = 0 (-36 + 4r + (-9r + r2)) = 0 Combine like terms: 4r + -9r = -5r (-36 + -5r + r2) = 0 Solving -36 + -5r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (-4 + -1r)(9 + -1r) = 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 '(9 + -1r)' equal to zero and attempt to solve: Simplifying 9 + -1r = 0 Solving 9 + -1r = 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 + -1r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1r = 0 + -9 -1r = 0 + -9 Combine like terms: 0 + -9 = -9 -1r = -9 Divide each side by '-1'. r = 9 Simplifying r = 9Solution
r = {-4, 9}
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