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Simplifying 25ab4 + -25az4 = 0 Solving 25ab4 + -25az4 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '25a'. 25a(b4 + -1z4) = 0 Factor a difference between two squares. 25a((b2 + z2)(b2 + -1z2)) = 0 Factor a difference between two squares. 25a((b2 + z2)((b + z)(b + -1z))) = 0 Ignore the factor 25.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(b2 + z2)' equal to zero and attempt to solve: Simplifying b2 + z2 = 0 Solving b2 + z2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b2' to each side of the equation. b2 + -1b2 + z2 = 0 + -1b2 Combine like terms: b2 + -1b2 = 0 0 + z2 = 0 + -1b2 z2 = 0 + -1b2 Remove the zero: z2 = -1b2 Add '-1z2' to each side of the equation. z2 + -1z2 = -1b2 + -1z2 Combine like terms: z2 + -1z2 = 0 0 = -1b2 + -1z2 Simplifying 0 = -1b2 + -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 '(b + z)' equal to zero and attempt to solve: Simplifying b + z = 0 Solving b + z = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. b + -1b + z = 0 + -1b Combine like terms: b + -1b = 0 0 + z = 0 + -1b z = 0 + -1b Remove the zero: z = -1b Add '-1z' to each side of the equation. z + -1z = -1b + -1z Combine like terms: z + -1z = 0 0 = -1b + -1z Simplifying 0 = -1b + -1z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(b + -1z)' equal to zero and attempt to solve: Simplifying b + -1z = 0 Solving b + -1z = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. b + -1b + -1z = 0 + -1b Combine like terms: b + -1b = 0 0 + -1z = 0 + -1b -1z = 0 + -1b Remove the zero: -1z = -1b Add 'z' to each side of the equation. -1z + z = -1b + z Combine like terms: -1z + z = 0 0 = -1b + z Simplifying 0 = -1b + z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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