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Simplifying 2z(z + -3)(z + -9) = 0 Reorder the terms: 2z(-3 + z)(z + -9) = 0 Reorder the terms: 2z(-3 + z)(-9 + z) = 0 Multiply (-3 + z) * (-9 + z) 2z(-3(-9 + z) + z(-9 + z)) = 0 2z((-9 * -3 + z * -3) + z(-9 + z)) = 0 2z((27 + -3z) + z(-9 + z)) = 0 2z(27 + -3z + (-9 * z + z * z)) = 0 2z(27 + -3z + (-9z + z2)) = 0 Combine like terms: -3z + -9z = -12z 2z(27 + -12z + z2) = 0 (27 * 2z + -12z * 2z + z2 * 2z) = 0 (54z + -24z2 + 2z3) = 0 Solving 54z + -24z2 + 2z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(27 + -12z + z2) = 0 Factor a trinomial. 2z((3 + -1z)(9 + -1z)) = 0 Ignore the factor 2.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 '(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 = 3Subproblem 3
Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9Solution
z = {0, 3, 9}
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