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Simplifying 80z8 + -45z6 = 0 Reorder the terms: -45z6 + 80z8 = 0 Solving -45z6 + 80z8 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z6'. 5z6(-9 + 16z2) = 0 Factor a difference between two squares. 5z6((3 + 4z)(-3 + 4z)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'z6' equal to zero and attempt to solve: Simplifying z6 = 0 Solving z6 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z6 = 0 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 '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 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 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75Subproblem 3
Set the factor '(-3 + 4z)' equal to zero and attempt to solve: Simplifying -3 + 4z = 0 Solving -3 + 4z = 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 + 4z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4z = 0 + 3 4z = 0 + 3 Combine like terms: 0 + 3 = 3 4z = 3 Divide each side by '4'. z = 0.75 Simplifying z = 0.75Solution
z = {-0.75, 0.75}
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