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Simplifying 54z3 + 27z2 + -13z = 29z Reorder the terms: -13z + 27z2 + 54z3 = 29z Solving -13z + 27z2 + 54z3 = 29z Solving for variable 'z'. Reorder the terms: -13z + -29z + 27z2 + 54z3 = 29z + -29z Combine like terms: -13z + -29z = -42z -42z + 27z2 + 54z3 = 29z + -29z Combine like terms: 29z + -29z = 0 -42z + 27z2 + 54z3 = 0 Factor out the Greatest Common Factor (GCF), '3z'. 3z(-14 + 9z + 18z2) = 0 Factor a trinomial. 3z((-7 + -6z)(2 + -3z)) = 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 '(-7 + -6z)' equal to zero and attempt to solve: Simplifying -7 + -6z = 0 Solving -7 + -6z = 0 Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -6z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6z = 0 + 7 -6z = 0 + 7 Combine like terms: 0 + 7 = 7 -6z = 7 Divide each side by '-6'. z = -1.166666667 Simplifying z = -1.166666667Subproblem 3
Set the factor '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667Solution
z = {0, -1.166666667, 0.6666666667}
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