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Simplifying z(z + -1)(z + 3) = 0 Reorder the terms: z(-1 + z)(z + 3) = 0 Reorder the terms: z(-1 + z)(3 + z) = 0 Multiply (-1 + z) * (3 + z) z(-1(3 + z) + z(3 + z)) = 0 z((3 * -1 + z * -1) + z(3 + z)) = 0 z((-3 + -1z) + z(3 + z)) = 0 z(-3 + -1z + (3 * z + z * z)) = 0 z(-3 + -1z + (3z + z2)) = 0 Combine like terms: -1z + 3z = 2z z(-3 + 2z + z2) = 0 (-3 * z + 2z * z + z2 * z) = 0 (-3z + 2z2 + z3) = 0 Solving -3z + 2z2 + z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-3 + 2z + z2) = 0 Factor a trinomial. z((-3 + -1z)(1 + -1z)) = 0Subproblem 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 '(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 = 1Solution
z = {0, -3, 1}
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