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Simplifying z3 + -12z2 + 48z = 0 Reorder the terms: 48z + -12z2 + z3 = 0 Solving 48z + -12z2 + z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(48 + -12z + 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 '(48 + -12z + z2)' equal to zero and attempt to solve: Simplifying 48 + -12z + z2 = 0 Solving 48 + -12z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -12z + -48 + z2 = 0 + -48 Reorder the terms: 48 + -48 + -12z + z2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -12z + z2 = 0 + -48 -12z + z2 = 0 + -48 Combine like terms: 0 + -48 = -48 -12z + z2 = -48 The z term is -12z. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12z + 36 + z2 = -48 + 36 Reorder the terms: 36 + -12z + z2 = -48 + 36 Combine like terms: -48 + 36 = -12 36 + -12z + z2 = -12 Factor a perfect square on the left side: (z + -6)(z + -6) = -12 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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