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Simplifying 6z2 + -8z + 1 = 1 Reorder the terms: 1 + -8z + 6z2 = 1 Add '-1' to each side of the equation. 1 + -8z + -1 + 6z2 = 1 + -1 Reorder the terms: 1 + -1 + -8z + 6z2 = 1 + -1 Combine like terms: 1 + -1 = 0 0 + -8z + 6z2 = 1 + -1 -8z + 6z2 = 1 + -1 Combine like terms: 1 + -1 = 0 -8z + 6z2 = 0 Solving -8z + 6z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(-4 + 3z) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(-4 + 3z)' equal to zero and attempt to solve: Simplifying -4 + 3z = 0 Solving -4 + 3z = 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 + 3z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3z = 0 + 4 3z = 0 + 4 Combine like terms: 0 + 4 = 4 3z = 4 Divide each side by '3'. z = 1.333333333 Simplifying z = 1.333333333Solution
z = {0, 1.333333333}
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