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Simplifying 12r2 + 7r + 15 = 9 + 10r2 Reorder the terms: 15 + 7r + 12r2 = 9 + 10r2 Solving 15 + 7r + 12r2 = 9 + 10r2 Solving for variable 'r'. Reorder the terms: 15 + -9 + 7r + 12r2 + -10r2 = 9 + 10r2 + -9 + -10r2 Combine like terms: 15 + -9 = 6 6 + 7r + 12r2 + -10r2 = 9 + 10r2 + -9 + -10r2 Combine like terms: 12r2 + -10r2 = 2r2 6 + 7r + 2r2 = 9 + 10r2 + -9 + -10r2 Reorder the terms: 6 + 7r + 2r2 = 9 + -9 + 10r2 + -10r2 Combine like terms: 9 + -9 = 0 6 + 7r + 2r2 = 0 + 10r2 + -10r2 6 + 7r + 2r2 = 10r2 + -10r2 Combine like terms: 10r2 + -10r2 = 0 6 + 7r + 2r2 = 0 Factor a trinomial. (2 + r)(3 + 2r) = 0Subproblem 1
Set the factor '(2 + r)' equal to zero and attempt to solve: Simplifying 2 + r = 0 Solving 2 + r = 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 + r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + r = 0 + -2 r = 0 + -2 Combine like terms: 0 + -2 = -2 r = -2 Simplifying r = -2Subproblem 2
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 = -1.5Solution
r = {-2, -1.5}
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