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Simplifying z(z + 6)(6z + 1) = 0 Reorder the terms: z(6 + z)(6z + 1) = 0 Reorder the terms: z(6 + z)(1 + 6z) = 0 Multiply (6 + z) * (1 + 6z) z(6(1 + 6z) + z(1 + 6z)) = 0 z((1 * 6 + 6z * 6) + z(1 + 6z)) = 0 z((6 + 36z) + z(1 + 6z)) = 0 z(6 + 36z + (1 * z + 6z * z)) = 0 z(6 + 36z + (1z + 6z2)) = 0 Combine like terms: 36z + 1z = 37z z(6 + 37z + 6z2) = 0 (6 * z + 37z * z + 6z2 * z) = 0 (6z + 37z2 + 6z3) = 0 Solving 6z + 37z2 + 6z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(6 + 37z + 6z2) = 0 Factor a trinomial. z((6 + z)(1 + 6z)) = 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 '(6 + z)' equal to zero and attempt to solve: Simplifying 6 + z = 0 Solving 6 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + z = 0 + -6 z = 0 + -6 Combine like terms: 0 + -6 = -6 z = -6 Simplifying z = -6Subproblem 3
Set the factor '(1 + 6z)' equal to zero and attempt to solve: Simplifying 1 + 6z = 0 Solving 1 + 6z = 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 + 6z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6z = 0 + -1 6z = 0 + -1 Combine like terms: 0 + -1 = -1 6z = -1 Divide each side by '6'. z = -0.1666666667 Simplifying z = -0.1666666667Solution
z = {0, -6, -0.1666666667}
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