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Simplifying 4r2 + -5r + -21 = 0 Reorder the terms: -21 + -5r + 4r2 = 0 Solving -21 + -5r + 4r2 = 0 Solving for variable 'r'. Factor a trinomial. (-7 + -4r)(3 + -1r) = 0Subproblem 1
Set the factor '(-7 + -4r)' equal to zero and attempt to solve: Simplifying -7 + -4r = 0 Solving -7 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4r = 0 + 7 -4r = 0 + 7 Combine like terms: 0 + 7 = 7 -4r = 7 Divide each side by '-4'. r = -1.75 Simplifying r = -1.75Subproblem 2
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 = {-1.75, 3}
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