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Simplifying r(z2 + 8)(z2 + 8) = 0 Reorder the terms: r(8 + z2)(z2 + 8) = 0 Reorder the terms: r(8 + z2)(8 + z2) = 0 Multiply (8 + z2) * (8 + z2) r(8(8 + z2) + z2(8 + z2)) = 0 r((8 * 8 + z2 * 8) + z2(8 + z2)) = 0 r((64 + 8z2) + z2(8 + z2)) = 0 r(64 + 8z2 + (8 * z2 + z2 * z2)) = 0 r(64 + 8z2 + (8z2 + z4)) = 0 Combine like terms: 8z2 + 8z2 = 16z2 r(64 + 16z2 + z4) = 0 (64 * r + 16z2 * r + z4 * r) = 0 (64r + 16rz2 + rz4) = 0 Solving 64r + 16rz2 + rz4 = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'r'. r(64 + 16z2 + z4) = 0 Factor a trinomial. r((8 + z2)(8 + z2)) = 0Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(8 + z2)' equal to zero and attempt to solve: Simplifying 8 + z2 = 0 Solving 8 + z2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + z2 = 0 + -8 z2 = 0 + -8 Combine like terms: 0 + -8 = -8 z2 = -8 Add '-1z2' to each side of the equation. z2 + -1z2 = -8 + -1z2 Combine like terms: z2 + -1z2 = 0 0 = -8 + -1z2 Simplifying 0 = -8 + -1z2 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 '(8 + z2)' equal to zero and attempt to solve: Simplifying 8 + z2 = 0 Solving 8 + z2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + z2 = 0 + -8 z2 = 0 + -8 Combine like terms: 0 + -8 = -8 z2 = -8 Add '-1z2' to each side of the equation. z2 + -1z2 = -8 + -1z2 Combine like terms: z2 + -1z2 = 0 0 = -8 + -1z2 Simplifying 0 = -8 + -1z2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
r = {0}
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