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Simplifying (6r2 + -4r4) + -1(3r2 + 4r4) = 0 Remove parenthesis around (6r2 + -4r4) 6r2 + -4r4 + -1(3r2 + 4r4) = 0 6r2 + -4r4 + (3r2 * -1 + 4r4 * -1) = 0 6r2 + -4r4 + (-3r2 + -4r4) = 0 Reorder the terms: 6r2 + -3r2 + -4r4 + -4r4 = 0 Combine like terms: 6r2 + -3r2 = 3r2 3r2 + -4r4 + -4r4 = 0 Combine like terms: -4r4 + -4r4 = -8r4 3r2 + -8r4 = 0 Solving 3r2 + -8r4 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r2'. r2(3 + -8r2) = 0Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r2 = 0 Take the square root of each side: r = {0}Subproblem 2
Set the factor '(3 + -8r2)' equal to zero and attempt to solve: Simplifying 3 + -8r2 = 0 Solving 3 + -8r2 = 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 + -8r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8r2 = 0 + -3 -8r2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8r2 = -3 Divide each side by '-8'. r2 = 0.375 Simplifying r2 = 0.375 Take the square root of each side: r = {-0.612372436, 0.612372436}Solution
r = {0, -0.612372436, 0.612372436}
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