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Simplifying (3z + -1)(8 + -1z) = 0 Reorder the terms: (-1 + 3z)(8 + -1z) = 0 Multiply (-1 + 3z) * (8 + -1z) (-1(8 + -1z) + 3z * (8 + -1z)) = 0 ((8 * -1 + -1z * -1) + 3z * (8 + -1z)) = 0 ((-8 + 1z) + 3z * (8 + -1z)) = 0 (-8 + 1z + (8 * 3z + -1z * 3z)) = 0 (-8 + 1z + (24z + -3z2)) = 0 Combine like terms: 1z + 24z = 25z (-8 + 25z + -3z2) = 0 Solving -8 + 25z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + z)(1 + -3z) = 0Subproblem 1
Set the factor '(-8 + z)' equal to zero and attempt to solve: Simplifying -8 + z = 0 Solving -8 + z = 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 + z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + z = 0 + 8 z = 0 + 8 Combine like terms: 0 + 8 = 8 z = 8 Simplifying z = 8Subproblem 2
Set the factor '(1 + -3z)' equal to zero and attempt to solve: Simplifying 1 + -3z = 0 Solving 1 + -3z = 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 + -3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3z = 0 + -1 -3z = 0 + -1 Combine like terms: 0 + -1 = -1 -3z = -1 Divide each side by '-3'. z = 0.3333333333 Simplifying z = 0.3333333333Solution
z = {8, 0.3333333333}
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