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Simplifying z6 + -4z3 = 5z3 + -18 Reorder the terms: -4z3 + z6 = 5z3 + -18 Reorder the terms: -4z3 + z6 = -18 + 5z3 Solving -4z3 + z6 = -18 + 5z3 Solving for variable 'z'. Reorder the terms: 18 + -4z3 + -5z3 + z6 = -18 + 5z3 + 18 + -5z3 Combine like terms: -4z3 + -5z3 = -9z3 18 + -9z3 + z6 = -18 + 5z3 + 18 + -5z3 Reorder the terms: 18 + -9z3 + z6 = -18 + 18 + 5z3 + -5z3 Combine like terms: -18 + 18 = 0 18 + -9z3 + z6 = 0 + 5z3 + -5z3 18 + -9z3 + z6 = 5z3 + -5z3 Combine like terms: 5z3 + -5z3 = 0 18 + -9z3 + z6 = 0 Factor a trinomial. (3 + -1z3)(6 + -1z3) = 0Subproblem 1
Set the factor '(3 + -1z3)' equal to zero and attempt to solve: Simplifying 3 + -1z3 = 0 Solving 3 + -1z3 = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z3 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z3 = 0 + -3 -1z3 = 0 + -3 Combine like terms: 0 + -3 = -3 -1z3 = -3 Divide each side by '-1'. z3 = 3 Simplifying z3 = 3 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 '(6 + -1z3)' equal to zero and attempt to solve: Simplifying 6 + -1z3 = 0 Solving 6 + -1z3 = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1z3 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1z3 = 0 + -6 -1z3 = 0 + -6 Combine like terms: 0 + -6 = -6 -1z3 = -6 Divide each side by '-1'. z3 = 6 Simplifying z3 = 6 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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