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Simplifying z3 + -3z2 + 7z = 0 Reorder the terms: 7z + -3z2 + z3 = 0 Solving 7z + -3z2 + z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(7 + -3z + z2) = 0Subproblem 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 '(7 + -3z + z2)' equal to zero and attempt to solve: Simplifying 7 + -3z + z2 = 0 Solving 7 + -3z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -3z + -7 + z2 = 0 + -7 Reorder the terms: 7 + -7 + -3z + z2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3z + z2 = 0 + -7 -3z + z2 = 0 + -7 Combine like terms: 0 + -7 = -7 -3z + z2 = -7 The z term is -3z. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3z + 2.25 + z2 = -7 + 2.25 Reorder the terms: 2.25 + -3z + z2 = -7 + 2.25 Combine like terms: -7 + 2.25 = -4.75 2.25 + -3z + z2 = -4.75 Factor a perfect square on the left side: (z + -1.5)(z + -1.5) = -4.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
z = {0}
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