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Simplifying (6r + 13)(r + 12) = 0 Reorder the terms: (13 + 6r)(r + 12) = 0 Reorder the terms: (13 + 6r)(12 + r) = 0 Multiply (13 + 6r) * (12 + r) (13(12 + r) + 6r * (12 + r)) = 0 ((12 * 13 + r * 13) + 6r * (12 + r)) = 0 ((156 + 13r) + 6r * (12 + r)) = 0 (156 + 13r + (12 * 6r + r * 6r)) = 0 (156 + 13r + (72r + 6r2)) = 0 Combine like terms: 13r + 72r = 85r (156 + 85r + 6r2) = 0 Solving 156 + 85r + 6r2 = 0 Solving for variable 'r'. Factor a trinomial. (12 + r)(13 + 6r) = 0Subproblem 1
Set the factor '(12 + r)' equal to zero and attempt to solve: Simplifying 12 + r = 0 Solving 12 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + r = 0 + -12 r = 0 + -12 Combine like terms: 0 + -12 = -12 r = -12 Simplifying r = -12Subproblem 2
Set the factor '(13 + 6r)' equal to zero and attempt to solve: Simplifying 13 + 6r = 0 Solving 13 + 6r = 0 Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 6r = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 6r = 0 + -13 6r = 0 + -13 Combine like terms: 0 + -13 = -13 6r = -13 Divide each side by '6'. r = -2.166666667 Simplifying r = -2.166666667Solution
r = {-12, -2.166666667}
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