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Simplifying (7r + 4)(2r + -6) = 0 Reorder the terms: (4 + 7r)(2r + -6) = 0 Reorder the terms: (4 + 7r)(-6 + 2r) = 0 Multiply (4 + 7r) * (-6 + 2r) (4(-6 + 2r) + 7r * (-6 + 2r)) = 0 ((-6 * 4 + 2r * 4) + 7r * (-6 + 2r)) = 0 ((-24 + 8r) + 7r * (-6 + 2r)) = 0 (-24 + 8r + (-6 * 7r + 2r * 7r)) = 0 (-24 + 8r + (-42r + 14r2)) = 0 Combine like terms: 8r + -42r = -34r (-24 + -34r + 14r2) = 0 Solving -24 + -34r + 14r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -17r + 7r2) = 0 Factor a trinomial. 2((-4 + -7r)(3 + -1r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -7r)' equal to zero and attempt to solve: Simplifying -4 + -7r = 0 Solving -4 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -7r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7r = 0 + 4 -7r = 0 + 4 Combine like terms: 0 + 4 = 4 -7r = 4 Divide each side by '-7'. r = -0.5714285714 Simplifying r = -0.5714285714Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 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 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {-0.5714285714, 3}
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