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Simplifying 7z2 + 5z4 = 12z6 Solving 7z2 + 5z4 = 12z6 Solving for variable 'z'. Combine like terms: 12z6 + -12z6 = 0 7z2 + 5z4 + -12z6 = 0 Factor out the Greatest Common Factor (GCF), 'z2'. z2(7 + 5z2 + -12z4) = 0 Factor a trinomial. z2((1 + -1z2)(7 + 12z2)) = 0 Factor a difference between two squares. z2(((1 + z)(1 + -1z))(7 + 12z2)) = 0Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}Subproblem 2
Set the factor '(7 + 12z2)' equal to zero and attempt to solve: Simplifying 7 + 12z2 = 0 Solving 7 + 12z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 12z2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 12z2 = 0 + -7 12z2 = 0 + -7 Combine like terms: 0 + -7 = -7 12z2 = -7 Divide each side by '12'. z2 = -0.5833333333 Simplifying z2 = -0.5833333333 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 '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Subproblem 4
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Solution
z = {0, -1, 1}
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