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Simplifying 12r2 + 21r + -8r + -14 = 0 Reorder the terms: -14 + 21r + -8r + 12r2 = 0 Combine like terms: 21r + -8r = 13r -14 + 13r + 12r2 = 0 Solving -14 + 13r + 12r2 = 0 Solving for variable 'r'. Factor a trinomial. (-7 + -4r)(2 + -3r) = 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 '(2 + -3r)' equal to zero and attempt to solve: Simplifying 2 + -3r = 0 Solving 2 + -3r = 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 + -3r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3r = 0 + -2 -3r = 0 + -2 Combine like terms: 0 + -2 = -2 -3r = -2 Divide each side by '-3'. r = 0.6666666667 Simplifying r = 0.6666666667Solution
r = {-1.75, 0.6666666667}
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