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Simplifying (-2r + 7)(6r + -3) = 0 Reorder the terms: (7 + -2r)(6r + -3) = 0 Reorder the terms: (7 + -2r)(-3 + 6r) = 0 Multiply (7 + -2r) * (-3 + 6r) (7(-3 + 6r) + -2r * (-3 + 6r)) = 0 ((-3 * 7 + 6r * 7) + -2r * (-3 + 6r)) = 0 ((-21 + 42r) + -2r * (-3 + 6r)) = 0 (-21 + 42r + (-3 * -2r + 6r * -2r)) = 0 (-21 + 42r + (6r + -12r2)) = 0 Combine like terms: 42r + 6r = 48r (-21 + 48r + -12r2) = 0 Solving -21 + 48r + -12r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 16r + -4r2) = 0 Factor a trinomial. 3((-7 + 2r)(1 + -2r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 2r)' equal to zero and attempt to solve: Simplifying -7 + 2r = 0 Solving -7 + 2r = 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 + 2r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2r = 0 + 7 2r = 0 + 7 Combine like terms: 0 + 7 = 7 2r = 7 Divide each side by '2'. r = 3.5 Simplifying r = 3.5Subproblem 2
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 = 0.5Solution
r = {3.5, 0.5}
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