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Simplifying 12z4 + -27z3 + -27z2 = 0 Reorder the terms: -27z2 + -27z3 + 12z4 = 0 Solving -27z2 + -27z3 + 12z4 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3z2'. 3z2(-9 + -9z + 4z2) = 0 Factor a trinomial. 3z2((-3 + -4z)(3 + -1z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}Subproblem 2
Set the factor '(-3 + -4z)' equal to zero and attempt to solve: Simplifying -3 + -4z = 0 Solving -3 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4z = 0 + 3 -4z = 0 + 3 Combine like terms: 0 + 3 = 3 -4z = 3 Divide each side by '-4'. z = -0.75 Simplifying z = -0.75Subproblem 3
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {0, -0.75, 3}
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