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