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Simplifying 4r2 = 24 + -10r Solving 4r2 = 24 + -10r Solving for variable 'r'. Reorder the terms: -24 + 10r + 4r2 = 24 + -10r + -24 + 10r Reorder the terms: -24 + 10r + 4r2 = 24 + -24 + -10r + 10r Combine like terms: 24 + -24 = 0 -24 + 10r + 4r2 = 0 + -10r + 10r -24 + 10r + 4r2 = -10r + 10r Combine like terms: -10r + 10r = 0 -24 + 10r + 4r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 5r + 2r2) = 0 Factor a trinomial. 2((-4 + -1r)(3 + -2r)) = 0 Ignore the factor 2.Subproblem 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 '(3 + -2r)' equal to zero and attempt to solve: Simplifying 3 + -2r = 0 Solving 3 + -2r = 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 + -2r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2r = 0 + -3 -2r = 0 + -3 Combine like terms: 0 + -3 = -3 -2r = -3 Divide each side by '-2'. r = 1.5 Simplifying r = 1.5Solution
r = {-4, 1.5}
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