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Simplifying (4r + 7) * 3 + -1(4r + 7) * 2r = 0 Reorder the terms: (7 + 4r) * 3 + -1(4r + 7) * 2r = 0 Reorder the terms for easier multiplication: 3(7 + 4r) + -1(4r + 7) * 2r = 0 (7 * 3 + 4r * 3) + -1(4r + 7) * 2r = 0 (21 + 12r) + -1(4r + 7) * 2r = 0 Reorder the terms: 21 + 12r + -1(7 + 4r) * 2r = 0 Reorder the terms for easier multiplication: 21 + 12r + -1 * 2r(7 + 4r) = 0 Multiply -1 * 2 21 + 12r + -2r(7 + 4r) = 0 21 + 12r + (7 * -2r + 4r * -2r) = 0 21 + 12r + (-14r + -8r2) = 0 Combine like terms: 12r + -14r = -2r 21 + -2r + -8r2 = 0 Solving 21 + -2r + -8r2 = 0 Solving for variable 'r'. Factor a trinomial. (3 + -2r)(7 + 4r) = 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 '(7 + 4r)' equal to zero and attempt to solve: Simplifying 7 + 4r = 0 Solving 7 + 4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4r = 0 + -7 4r = 0 + -7 Combine like terms: 0 + -7 = -7 4r = -7 Divide each side by '4'. r = -1.75 Simplifying r = -1.75Solution
r = {1.5, -1.75}
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