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Simplifying (6r + 1)(3r + -4) = 0 Reorder the terms: (1 + 6r)(3r + -4) = 0 Reorder the terms: (1 + 6r)(-4 + 3r) = 0 Multiply (1 + 6r) * (-4 + 3r) (1(-4 + 3r) + 6r * (-4 + 3r)) = 0 ((-4 * 1 + 3r * 1) + 6r * (-4 + 3r)) = 0 ((-4 + 3r) + 6r * (-4 + 3r)) = 0 (-4 + 3r + (-4 * 6r + 3r * 6r)) = 0 (-4 + 3r + (-24r + 18r2)) = 0 Combine like terms: 3r + -24r = -21r (-4 + -21r + 18r2) = 0 Solving -4 + -21r + 18r2 = 0 Solving for variable 'r'. Factor a trinomial. (-1 + -6r)(4 + -3r) = 0Subproblem 1
Set the factor '(-1 + -6r)' equal to zero and attempt to solve: Simplifying -1 + -6r = 0 Solving -1 + -6r = 0 Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -6r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6r = 0 + 1 -6r = 0 + 1 Combine like terms: 0 + 1 = 1 -6r = 1 Divide each side by '-6'. r = -0.1666666667 Simplifying r = -0.1666666667Subproblem 2
Set the factor '(4 + -3r)' equal to zero and attempt to solve: Simplifying 4 + -3r = 0 Solving 4 + -3r = 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 + -3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3r = 0 + -4 -3r = 0 + -4 Combine like terms: 0 + -4 = -4 -3r = -4 Divide each side by '-3'. r = 1.333333333 Simplifying r = 1.333333333Solution
r = {-0.1666666667, 1.333333333}
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