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Simplifying 2r2 = 12 + 5r Solving 2r2 = 12 + 5r Solving for variable 'r'. Reorder the terms: -12 + -5r + 2r2 = 12 + 5r + -12 + -5r Reorder the terms: -12 + -5r + 2r2 = 12 + -12 + 5r + -5r Combine like terms: 12 + -12 = 0 -12 + -5r + 2r2 = 0 + 5r + -5r -12 + -5r + 2r2 = 5r + -5r Combine like terms: 5r + -5r = 0 -12 + -5r + 2r2 = 0 Factor a trinomial. (-3 + -2r)(4 + -1r) = 0Subproblem 1
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 = -1.5Subproblem 2
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 = 4Solution
r = {-1.5, 4}
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