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Simplifying (r + 3)(r + -2) = 0 Reorder the terms: (3 + r)(r + -2) = 0 Reorder the terms: (3 + r)(-2 + r) = 0 Multiply (3 + r) * (-2 + r) (3(-2 + r) + r(-2 + r)) = 0 ((-2 * 3 + r * 3) + r(-2 + r)) = 0 ((-6 + 3r) + r(-2 + r)) = 0 (-6 + 3r + (-2 * r + r * r)) = 0 (-6 + 3r + (-2r + r2)) = 0 Combine like terms: 3r + -2r = 1r (-6 + 1r + r2) = 0 Solving -6 + 1r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (-3 + -1r)(2 + -1r) = 0Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve: Simplifying -3 + -1r = 0 Solving -3 + -1r = 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 + -1r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1r = 0 + 3 -1r = 0 + 3 Combine like terms: 0 + 3 = 3 -1r = 3 Divide each side by '-1'. r = -3 Simplifying r = -3Subproblem 2
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 = 2Solution
r = {-3, 2}
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