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Simplifying h3 + 6h2 + 12h = 0 Reorder the terms: 12h + 6h2 + h3 = 0 Solving 12h + 6h2 + h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), 'h'. h(12 + 6h + h2) = 0Subproblem 1
Set the factor 'h' equal to zero and attempt to solve: Simplifying h = 0 Solving h = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h = 0Subproblem 2
Set the factor '(12 + 6h + h2)' equal to zero and attempt to solve: Simplifying 12 + 6h + h2 = 0 Solving 12 + 6h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 6h + -12 + h2 = 0 + -12 Reorder the terms: 12 + -12 + 6h + h2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 6h + h2 = 0 + -12 6h + h2 = 0 + -12 Combine like terms: 0 + -12 = -12 6h + h2 = -12 The h term is 6h. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6h + 9 + h2 = -12 + 9 Reorder the terms: 9 + 6h + h2 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + 6h + h2 = -3 Factor a perfect square on the left side: (h + 3)(h + 3) = -3 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
h = {0}
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