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Simplifying (7r + 5)(2r + -3) = 0 Reorder the terms: (5 + 7r)(2r + -3) = 0 Reorder the terms: (5 + 7r)(-3 + 2r) = 0 Multiply (5 + 7r) * (-3 + 2r) (5(-3 + 2r) + 7r * (-3 + 2r)) = 0 ((-3 * 5 + 2r * 5) + 7r * (-3 + 2r)) = 0 ((-15 + 10r) + 7r * (-3 + 2r)) = 0 (-15 + 10r + (-3 * 7r + 2r * 7r)) = 0 (-15 + 10r + (-21r + 14r2)) = 0 Combine like terms: 10r + -21r = -11r (-15 + -11r + 14r2) = 0 Solving -15 + -11r + 14r2 = 0 Solving for variable 'r'. Factor a trinomial. (-5 + -7r)(3 + -2r) = 0Subproblem 1
Set the factor '(-5 + -7r)' equal to zero and attempt to solve: Simplifying -5 + -7r = 0 Solving -5 + -7r = 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 + -7r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7r = 0 + 5 -7r = 0 + 5 Combine like terms: 0 + 5 = 5 -7r = 5 Divide each side by '-7'. r = -0.7142857143 Simplifying r = -0.7142857143Subproblem 2
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 = 1.5Solution
r = {-0.7142857143, 1.5}
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