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Simplifying r(r + -2)(r + -3) = 0 Reorder the terms: r(-2 + r)(r + -3) = 0 Reorder the terms: r(-2 + r)(-3 + r) = 0 Multiply (-2 + r) * (-3 + r) r(-2(-3 + r) + r(-3 + r)) = 0 r((-3 * -2 + r * -2) + r(-3 + r)) = 0 r((6 + -2r) + r(-3 + r)) = 0 r(6 + -2r + (-3 * r + r * r)) = 0 r(6 + -2r + (-3r + r2)) = 0 Combine like terms: -2r + -3r = -5r r(6 + -5r + r2) = 0 (6 * r + -5r * r + r2 * r) = 0 (6r + -5r2 + r3) = 0 Solving 6r + -5r2 + r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(6 + -5r + r2) = 0 Factor a trinomial. r((2 + -1r)(3 + -1r)) = 0Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 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 = 2Subproblem 3
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 = 3Solution
r = {0, 2, 3}
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