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Simplifying 8z + -3z3 + 12z = 0 Reorder the terms: 8z + 12z + -3z3 = 0 Combine like terms: 8z + 12z = 20z 20z + -3z3 = 0 Solving 20z + -3z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(20 + -3z2) = 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 '(20 + -3z2)' equal to zero and attempt to solve: Simplifying 20 + -3z2 = 0 Solving 20 + -3z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -3z2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -3z2 = 0 + -20 -3z2 = 0 + -20 Combine like terms: 0 + -20 = -20 -3z2 = -20 Divide each side by '-3'. z2 = 6.666666667 Simplifying z2 = 6.666666667 Take the square root of each side: z = {-2.581988898, 2.581988898}Solution
z = {0, -2.581988898, 2.581988898}
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