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Simplifying 3z3 + -135z2 + -588z = 0 Reorder the terms: -588z + -135z2 + 3z3 = 0 Solving -588z + -135z2 + 3z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3z'. 3z(-196 + -45z + z2) = 0 Factor a trinomial. 3z((-4 + -1z)(49 + -1z)) = 0 Ignore the factor 3.Subproblem 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 '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4Subproblem 3
Set the factor '(49 + -1z)' equal to zero and attempt to solve: Simplifying 49 + -1z = 0 Solving 49 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + -49 + -1z = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -1z = 0 + -49 -1z = 0 + -49 Combine like terms: 0 + -49 = -49 -1z = -49 Divide each side by '-1'. z = 49 Simplifying z = 49Solution
z = {0, -4, 49}
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