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Simplifying 2r(3r + -4) + -5(r + -1) = 0 Reorder the terms: 2r(-4 + 3r) + -5(r + -1) = 0 (-4 * 2r + 3r * 2r) + -5(r + -1) = 0 (-8r + 6r2) + -5(r + -1) = 0 Reorder the terms: -8r + 6r2 + -5(-1 + r) = 0 -8r + 6r2 + (-1 * -5 + r * -5) = 0 -8r + 6r2 + (5 + -5r) = 0 Reorder the terms: 5 + -8r + -5r + 6r2 = 0 Combine like terms: -8r + -5r = -13r 5 + -13r + 6r2 = 0 Solving 5 + -13r + 6r2 = 0 Solving for variable 'r'. Factor a trinomial. (1 + -2r)(5 + -3r) = 0Subproblem 1
Set the factor '(1 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 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 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Subproblem 2
Set the factor '(5 + -3r)' equal to zero and attempt to solve: Simplifying 5 + -3r = 0 Solving 5 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3r = 0 + -5 -3r = 0 + -5 Combine like terms: 0 + -5 = -5 -3r = -5 Divide each side by '-3'. r = 1.666666667 Simplifying r = 1.666666667Solution
r = {0.5, 1.666666667}
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