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Simplifying 3z3 = -1z2 + 2z Reorder the terms: 3z3 = 2z + -1z2 Solving 3z3 = 2z + -1z2 Solving for variable 'z'. Reorder the terms: -2z + z2 + 3z3 = 2z + -1z2 + -2z + z2 Reorder the terms: -2z + z2 + 3z3 = 2z + -2z + -1z2 + z2 Combine like terms: 2z + -2z = 0 -2z + z2 + 3z3 = 0 + -1z2 + z2 -2z + z2 + 3z3 = -1z2 + z2 Combine like terms: -1z2 + z2 = 0 -2z + z2 + 3z3 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(-2 + z + 3z2) = 0 Factor a trinomial. z((-1 + -1z)(2 + -3z)) = 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 '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1Subproblem 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, 0.6666666667}
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