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Simplifying z(4z + 5)(z + 4) = 0 Reorder the terms: z(5 + 4z)(z + 4) = 0 Reorder the terms: z(5 + 4z)(4 + z) = 0 Multiply (5 + 4z) * (4 + z) z(5(4 + z) + 4z * (4 + z)) = 0 z((4 * 5 + z * 5) + 4z * (4 + z)) = 0 z((20 + 5z) + 4z * (4 + z)) = 0 z(20 + 5z + (4 * 4z + z * 4z)) = 0 z(20 + 5z + (16z + 4z2)) = 0 Combine like terms: 5z + 16z = 21z z(20 + 21z + 4z2) = 0 (20 * z + 21z * z + 4z2 * z) = 0 (20z + 21z2 + 4z3) = 0 Solving 20z + 21z2 + 4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(20 + 21z + 4z2) = 0 Factor a trinomial. z((4 + z)(5 + 4z)) = 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 '(4 + z)' equal to zero and attempt to solve: Simplifying 4 + z = 0 Solving 4 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z = 0 + -4 z = 0 + -4 Combine like terms: 0 + -4 = -4 z = -4 Simplifying z = -4Subproblem 3
Set the factor '(5 + 4z)' equal to zero and attempt to solve: Simplifying 5 + 4z = 0 Solving 5 + 4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4z = 0 + -5 4z = 0 + -5 Combine like terms: 0 + -5 = -5 4z = -5 Divide each side by '4'. z = -1.25 Simplifying z = -1.25Solution
z = {0, -4, -1.25}
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