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Simplifying r(r + -3)(r + 5) = 0 Reorder the terms: r(-3 + r)(r + 5) = 0 Reorder the terms: r(-3 + r)(5 + r) = 0 Multiply (-3 + r) * (5 + r) r(-3(5 + r) + r(5 + r)) = 0 r((5 * -3 + r * -3) + r(5 + r)) = 0 r((-15 + -3r) + r(5 + r)) = 0 r(-15 + -3r + (5 * r + r * r)) = 0 r(-15 + -3r + (5r + r2)) = 0 Combine like terms: -3r + 5r = 2r r(-15 + 2r + r2) = 0 (-15 * r + 2r * r + r2 * r) = 0 (-15r + 2r2 + r3) = 0 Solving -15r + 2r2 + r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-15 + 2r + r2) = 0 Factor a trinomial. r((-5 + -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 '(-5 + -1r)' equal to zero and attempt to solve: Simplifying -5 + -1r = 0 Solving -5 + -1r = 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 + -1r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1r = 0 + 5 -1r = 0 + 5 Combine like terms: 0 + 5 = 5 -1r = 5 Divide each side by '-1'. r = -5 Simplifying r = -5Subproblem 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, -5, 3}
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