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Simplifying (10R + 7)(3R + -5) = 0 Reorder the terms: (7 + 10R)(3R + -5) = 0 Reorder the terms: (7 + 10R)(-5 + 3R) = 0 Multiply (7 + 10R) * (-5 + 3R) (7(-5 + 3R) + 10R * (-5 + 3R)) = 0 ((-5 * 7 + 3R * 7) + 10R * (-5 + 3R)) = 0 ((-35 + 21R) + 10R * (-5 + 3R)) = 0 (-35 + 21R + (-5 * 10R + 3R * 10R)) = 0 (-35 + 21R + (-50R + 30R2)) = 0 Combine like terms: 21R + -50R = -29R (-35 + -29R + 30R2) = 0 Solving -35 + -29R + 30R2 = 0 Solving for variable 'R'. Factor a trinomial. (-7 + -10R)(5 + -3R) = 0Subproblem 1
Set the factor '(-7 + -10R)' equal to zero and attempt to solve: Simplifying -7 + -10R = 0 Solving -7 + -10R = 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 + -10R = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10R = 0 + 7 -10R = 0 + 7 Combine like terms: 0 + 7 = 7 -10R = 7 Divide each side by '-10'. R = -0.7 Simplifying R = -0.7Subproblem 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 = {-0.7, 1.666666667}
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