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Simplifying (4z + 8)(z + -4) = 0 Reorder the terms: (8 + 4z)(z + -4) = 0 Reorder the terms: (8 + 4z)(-4 + z) = 0 Multiply (8 + 4z) * (-4 + z) (8(-4 + z) + 4z * (-4 + z)) = 0 ((-4 * 8 + z * 8) + 4z * (-4 + z)) = 0 ((-32 + 8z) + 4z * (-4 + z)) = 0 (-32 + 8z + (-4 * 4z + z * 4z)) = 0 (-32 + 8z + (-16z + 4z2)) = 0 Combine like terms: 8z + -16z = -8z (-32 + -8z + 4z2) = 0 Solving -32 + -8z + 4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + -2z + z2) = 0 Factor a trinomial. 4((-2 + -1z)(4 + -1z)) = 0 Ignore the factor 4.Subproblem 1
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 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 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 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Solution
z = {-2, 4}
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