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Simplifying 2z(3z + 4)(4z + -6) = 0 Reorder the terms: 2z(4 + 3z)(4z + -6) = 0 Reorder the terms: 2z(4 + 3z)(-6 + 4z) = 0 Multiply (4 + 3z) * (-6 + 4z) 2z(4(-6 + 4z) + 3z * (-6 + 4z)) = 0 2z((-6 * 4 + 4z * 4) + 3z * (-6 + 4z)) = 0 2z((-24 + 16z) + 3z * (-6 + 4z)) = 0 2z(-24 + 16z + (-6 * 3z + 4z * 3z)) = 0 2z(-24 + 16z + (-18z + 12z2)) = 0 Combine like terms: 16z + -18z = -2z 2z(-24 + -2z + 12z2) = 0 (-24 * 2z + -2z * 2z + 12z2 * 2z) = 0 (-48z + -4z2 + 24z3) = 0 Solving -48z + -4z2 + 24z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z'. 4z(-12 + -1z + 6z2) = 0 Factor a trinomial. 4z((-4 + -3z)(3 + -2z)) = 0 Ignore the factor 4.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 + -3z)' equal to zero and attempt to solve: Simplifying -4 + -3z = 0 Solving -4 + -3z = 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 + -3z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3z = 0 + 4 -3z = 0 + 4 Combine like terms: 0 + 4 = 4 -3z = 4 Divide each side by '-3'. z = -1.333333333 Simplifying z = -1.333333333Subproblem 3
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 = 1.5Solution
z = {0, -1.333333333, 1.5}
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