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Simplifying 4r2 + -32r + -132 = 0 Reorder the terms: -132 + -32r + 4r2 = 0 Solving -132 + -32r + 4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(-33 + -8r + r2) = 0 Factor a trinomial. 4((-3 + -1r)(11 + -1r)) = 0 Ignore the factor 4.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 '(11 + -1r)' equal to zero and attempt to solve: Simplifying 11 + -1r = 0 Solving 11 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1r = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1r = 0 + -11 -1r = 0 + -11 Combine like terms: 0 + -11 = -11 -1r = -11 Divide each side by '-1'. r = 11 Simplifying r = 11Solution
r = {-3, 11}
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