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Simplifying z(z + -17)(z + 2) = 0 Reorder the terms: z(-17 + z)(z + 2) = 0 Reorder the terms: z(-17 + z)(2 + z) = 0 Multiply (-17 + z) * (2 + z) z(-17(2 + z) + z(2 + z)) = 0 z((2 * -17 + z * -17) + z(2 + z)) = 0 z((-34 + -17z) + z(2 + z)) = 0 z(-34 + -17z + (2 * z + z * z)) = 0 z(-34 + -17z + (2z + z2)) = 0 Combine like terms: -17z + 2z = -15z z(-34 + -15z + z2) = 0 (-34 * z + -15z * z + z2 * z) = 0 (-34z + -15z2 + z3) = 0 Solving -34z + -15z2 + z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-34 + -15z + z2) = 0 Factor a trinomial. z((-2 + -1z)(17 + -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 '(-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 '(17 + -1z)' equal to zero and attempt to solve: Simplifying 17 + -1z = 0 Solving 17 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1z = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1z = 0 + -17 -1z = 0 + -17 Combine like terms: 0 + -17 = -17 -1z = -17 Divide each side by '-1'. z = 17 Simplifying z = 17Solution
z = {0, -2, 17}
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