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Simplifying -3r3(9r2 + 6)(9r2 + -6) = 0 Reorder the terms: -3r3(6 + 9r2)(9r2 + -6) = 0 Reorder the terms: -3r3(6 + 9r2)(-6 + 9r2) = 0 Multiply (6 + 9r2) * (-6 + 9r2) -3r3(6(-6 + 9r2) + 9r2 * (-6 + 9r2)) = 0 -3r3((-6 * 6 + 9r2 * 6) + 9r2 * (-6 + 9r2)) = 0 -3r3((-36 + 54r2) + 9r2 * (-6 + 9r2)) = 0 -3r3(-36 + 54r2 + (-6 * 9r2 + 9r2 * 9r2)) = 0 -3r3(-36 + 54r2 + (-54r2 + 81r4)) = 0 Combine like terms: 54r2 + -54r2 = 0 -3r3(-36 + 0 + 81r4) = 0 -3r3(-36 + 81r4) = 0 (-36 * -3r3 + 81r4 * -3r3) = 0 (108r3 + -243r7) = 0 Solving 108r3 + -243r7 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '27r3'. 27r3(4 + -9r4) = 0 Factor a difference between two squares. 27r3((2 + 3r2)(2 + -3r2)) = 0 Ignore the factor 27.Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve: Simplifying r3 = 0 Solving r3 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + 3r2)' equal to zero and attempt to solve: Simplifying 2 + 3r2 = 0 Solving 2 + 3r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3r2 = 0 + -2 3r2 = 0 + -2 Combine like terms: 0 + -2 = -2 3r2 = -2 Divide each side by '3'. r2 = -0.6666666667 Simplifying r2 = -0.6666666667 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + -3r2)' equal to zero and attempt to solve: Simplifying 2 + -3r2 = 0 Solving 2 + -3r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3r2 = 0 + -2 -3r2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3r2 = -2 Divide each side by '-3'. r2 = 0.6666666667 Simplifying r2 = 0.6666666667 Take the square root of each side: r = {-0.816496581, 0.816496581}Solution
r = {-0.816496581, 0.816496581}
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