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Simplifying z6 + -4(z3) = 5(z3) + -20 Reorder the terms: -4z3 + z6 = 5(z3) + -20 Reorder the terms: -4z3 + z6 = -20 + 5z3 Solving -4z3 + z6 = -20 + 5z3 Solving for variable 'z'. Reorder the terms: 20 + -4z3 + -5z3 + z6 = -20 + 5z3 + 20 + -5z3 Combine like terms: -4z3 + -5z3 = -9z3 20 + -9z3 + z6 = -20 + 5z3 + 20 + -5z3 Reorder the terms: 20 + -9z3 + z6 = -20 + 20 + 5z3 + -5z3 Combine like terms: -20 + 20 = 0 20 + -9z3 + z6 = 0 + 5z3 + -5z3 20 + -9z3 + z6 = 5z3 + -5z3 Combine like terms: 5z3 + -5z3 = 0 20 + -9z3 + z6 = 0 Factor a trinomial. (4 + -1z3)(5 + -1z3) = 0Subproblem 1
Set the factor '(4 + -1z3)' equal to zero and attempt to solve: Simplifying 4 + -1z3 = 0 Solving 4 + -1z3 = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z3 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z3 = 0 + -4 -1z3 = 0 + -4 Combine like terms: 0 + -4 = -4 -1z3 = -4 Divide each side by '-1'. z3 = 4 Simplifying z3 = 4 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 '(5 + -1z3)' equal to zero and attempt to solve: Simplifying 5 + -1z3 = 0 Solving 5 + -1z3 = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z3 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z3 = 0 + -5 -1z3 = 0 + -5 Combine like terms: 0 + -5 = -5 -1z3 = -5 Divide each side by '-1'. z3 = 5 Simplifying z3 = 5 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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