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Simplifying -343z3 + 784z2 + -448z = 0 Reorder the terms: -448z + 784z2 + -343z3 = 0 Solving -448z + 784z2 + -343z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '7z'. 7z(-64 + 112z + -49z2) = 0 Factor a trinomial. 7z((-8 + 7z)(8 + -7z)) = 0 Ignore the factor 7.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 '(-8 + 7z)' equal to zero and attempt to solve: Simplifying -8 + 7z = 0 Solving -8 + 7z = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 7z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 7z = 0 + 8 7z = 0 + 8 Combine like terms: 0 + 8 = 8 7z = 8 Divide each side by '7'. z = 1.142857143 Simplifying z = 1.142857143Subproblem 3
Set the factor '(8 + -7z)' equal to zero and attempt to solve: Simplifying 8 + -7z = 0 Solving 8 + -7z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7z = 0 + -8 -7z = 0 + -8 Combine like terms: 0 + -8 = -8 -7z = -8 Divide each side by '-7'. z = 1.142857143 Simplifying z = 1.142857143Solution
z = {0, 1.142857143, 1.142857143}
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