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Simplifying 4r2 + 2r + -32 = -12 Reorder the terms: -32 + 2r + 4r2 = -12 Solving -32 + 2r + 4r2 = -12 Solving for variable 'r'. Reorder the terms: -32 + 12 + 2r + 4r2 = -12 + 12 Combine like terms: -32 + 12 = -20 -20 + 2r + 4r2 = -12 + 12 Combine like terms: -12 + 12 = 0 -20 + 2r + 4r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + r + 2r2) = 0 Factor a trinomial. 2((-5 + -2r)(2 + -1r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2r)' equal to zero and attempt to solve: Simplifying -5 + -2r = 0 Solving -5 + -2r = 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 + -2r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2r = 0 + 5 -2r = 0 + 5 Combine like terms: 0 + 5 = 5 -2r = 5 Divide each side by '-2'. r = -2.5 Simplifying r = -2.5Subproblem 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 = {-2.5, 2}
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