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Simplifying (z + -4)(z + -8) = 0 Reorder the terms: (-4 + z)(z + -8) = 0 Reorder the terms: (-4 + z)(-8 + z) = 0 Multiply (-4 + z) * (-8 + z) (-4(-8 + z) + z(-8 + z)) = 0 ((-8 * -4 + z * -4) + z(-8 + z)) = 0 ((32 + -4z) + z(-8 + z)) = 0 (32 + -4z + (-8 * z + z * z)) = 0 (32 + -4z + (-8z + z2)) = 0 Combine like terms: -4z + -8z = -12z (32 + -12z + z2) = 0 Solving 32 + -12z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + -1z)(8 + -1z) = 0Subproblem 1
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 = 4Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Solution
z = {4, 8}
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