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Simplifying (7r + 3)(4r + -3) = 0 Reorder the terms: (3 + 7r)(4r + -3) = 0 Reorder the terms: (3 + 7r)(-3 + 4r) = 0 Multiply (3 + 7r) * (-3 + 4r) (3(-3 + 4r) + 7r * (-3 + 4r)) = 0 ((-3 * 3 + 4r * 3) + 7r * (-3 + 4r)) = 0 ((-9 + 12r) + 7r * (-3 + 4r)) = 0 (-9 + 12r + (-3 * 7r + 4r * 7r)) = 0 (-9 + 12r + (-21r + 28r2)) = 0 Combine like terms: 12r + -21r = -9r (-9 + -9r + 28r2) = 0 Solving -9 + -9r + 28r2 = 0 Solving for variable 'r'. Factor a trinomial. (-3 + -7r)(3 + -4r) = 0Subproblem 1
Set the factor '(-3 + -7r)' equal to zero and attempt to solve: Simplifying -3 + -7r = 0 Solving -3 + -7r = 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 + -7r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7r = 0 + 3 -7r = 0 + 3 Combine like terms: 0 + 3 = 3 -7r = 3 Divide each side by '-7'. r = -0.4285714286 Simplifying r = -0.4285714286Subproblem 2
Set the factor '(3 + -4r)' equal to zero and attempt to solve: Simplifying 3 + -4r = 0 Solving 3 + -4r = 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 + -4r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4r = 0 + -3 -4r = 0 + -3 Combine like terms: 0 + -3 = -3 -4r = -3 Divide each side by '-4'. r = 0.75 Simplifying r = 0.75Solution
r = {-0.4285714286, 0.75}
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