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Simplifying 3z(2z + 3)(3z + -5) = 0 Reorder the terms: 3z(3 + 2z)(3z + -5) = 0 Reorder the terms: 3z(3 + 2z)(-5 + 3z) = 0 Multiply (3 + 2z) * (-5 + 3z) 3z(3(-5 + 3z) + 2z * (-5 + 3z)) = 0 3z((-5 * 3 + 3z * 3) + 2z * (-5 + 3z)) = 0 3z((-15 + 9z) + 2z * (-5 + 3z)) = 0 3z(-15 + 9z + (-5 * 2z + 3z * 2z)) = 0 3z(-15 + 9z + (-10z + 6z2)) = 0 Combine like terms: 9z + -10z = -1z 3z(-15 + -1z + 6z2) = 0 (-15 * 3z + -1z * 3z + 6z2 * 3z) = 0 (-45z + -3z2 + 18z3) = 0 Solving -45z + -3z2 + 18z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3z'. 3z(-15 + -1z + 6z2) = 0 Factor a trinomial. 3z((-3 + -2z)(5 + -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 '(-3 + -2z)' equal to zero and attempt to solve: Simplifying -3 + -2z = 0 Solving -3 + -2z = 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 + -2z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2z = 0 + 3 -2z = 0 + 3 Combine like terms: 0 + 3 = 3 -2z = 3 Divide each side by '-2'. z = -1.5 Simplifying z = -1.5Subproblem 3
Set the factor '(5 + -3z)' equal to zero and attempt to solve: Simplifying 5 + -3z = 0 Solving 5 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3z = 0 + -5 -3z = 0 + -5 Combine like terms: 0 + -5 = -5 -3z = -5 Divide each side by '-3'. z = 1.666666667 Simplifying z = 1.666666667Solution
z = {0, -1.5, 1.666666667}
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