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Simplifying 5(z + -1)(-1z + -4) = 0 Reorder the terms: 5(-1 + z)(-1z + -4) = 0 Reorder the terms: 5(-1 + z)(-4 + -1z) = 0 Multiply (-1 + z) * (-4 + -1z) 5(-1(-4 + -1z) + z(-4 + -1z)) = 0 5((-4 * -1 + -1z * -1) + z(-4 + -1z)) = 0 5((4 + 1z) + z(-4 + -1z)) = 0 5(4 + 1z + (-4 * z + -1z * z)) = 0 5(4 + 1z + (-4z + -1z2)) = 0 Combine like terms: 1z + -4z = -3z 5(4 + -3z + -1z2) = 0 (4 * 5 + -3z * 5 + -1z2 * 5) = 0 (20 + -15z + -5z2) = 0 Solving 20 + -15z + -5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(4 + -3z + -1z2) = 0 Factor a trinomial. 5((1 + -1z)(4 + z)) = 0 Ignore the factor 5.Subproblem 1
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 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 = -4Solution
z = {1, -4}
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