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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 = 5z 5(-4 + 5z + -1z2) = 0 (-4 * 5 + 5z * 5 + -1z2 * 5) = 0 (-20 + 25z + -5z2) = 0 Solving -20 + 25z + -5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + 5z + -1z2) = 0 Factor a trinomial. 5((-4 + z)(1 + -1z)) = 0 Ignore the factor 5.Subproblem 1
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 2
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 = {4, 1}
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