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Simplifying -5z(z + 2)(z + -1) = 0 Reorder the terms: -5z(2 + z)(z + -1) = 0 Reorder the terms: -5z(2 + z)(-1 + z) = 0 Multiply (2 + z) * (-1 + z) -5z(2(-1 + z) + z(-1 + z)) = 0 -5z((-1 * 2 + z * 2) + z(-1 + z)) = 0 -5z((-2 + 2z) + z(-1 + z)) = 0 -5z(-2 + 2z + (-1 * z + z * z)) = 0 -5z(-2 + 2z + (-1z + z2)) = 0 Combine like terms: 2z + -1z = 1z -5z(-2 + 1z + z2) = 0 (-2 * -5z + 1z * -5z + z2 * -5z) = 0 (10z + -5z2 + -5z3) = 0 Solving 10z + -5z2 + -5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z'. 5z(2 + -1z + -1z2) = 0 Factor a trinomial. 5z((1 + -1z)(2 + z)) = 0 Ignore the factor 5.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 '(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 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 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 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Solution
z = {0, 1, -2}
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