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Simplifying (r + -4)(2r + 6) = 0 Reorder the terms: (-4 + r)(2r + 6) = 0 Reorder the terms: (-4 + r)(6 + 2r) = 0 Multiply (-4 + r) * (6 + 2r) (-4(6 + 2r) + r(6 + 2r)) = 0 ((6 * -4 + 2r * -4) + r(6 + 2r)) = 0 ((-24 + -8r) + r(6 + 2r)) = 0 (-24 + -8r + (6 * r + 2r * r)) = 0 (-24 + -8r + (6r + 2r2)) = 0 Combine like terms: -8r + 6r = -2r (-24 + -2r + 2r2) = 0 Solving -24 + -2r + 2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -1r + r2) = 0 Factor a trinomial. 2((-3 + -1r)(4 + -1r)) = 0 Ignore the factor 2.Subproblem 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 '(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 = 4Solution
r = {-3, 4}
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