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Simplifying 2r * 4r + 8r + -6 = 0 Reorder the terms for easier multiplication: 2 * 4r * r + 8r + -6 = 0 Multiply 2 * 4 8r * r + 8r + -6 = 0 Multiply r * r 8r2 + 8r + -6 = 0 Reorder the terms: -6 + 8r + 8r2 = 0 Solving -6 + 8r + 8r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 4r + 4r2) = 0 Factor a trinomial. 2((-3 + -2r)(1 + -2r)) = 0 Ignore the factor 2.Subproblem 1
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 = -1.5Subproblem 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 = {-1.5, 0.5}
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