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Simplifying (3z + -8)(2 + -1z) = 0 Reorder the terms: (-8 + 3z)(2 + -1z) = 0 Multiply (-8 + 3z) * (2 + -1z) (-8(2 + -1z) + 3z * (2 + -1z)) = 0 ((2 * -8 + -1z * -8) + 3z * (2 + -1z)) = 0 ((-16 + 8z) + 3z * (2 + -1z)) = 0 (-16 + 8z + (2 * 3z + -1z * 3z)) = 0 (-16 + 8z + (6z + -3z2)) = 0 Combine like terms: 8z + 6z = 14z (-16 + 14z + -3z2) = 0 Solving -16 + 14z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + 3z)(2 + -1z) = 0Subproblem 1
Set the factor '(-8 + 3z)' equal to zero and attempt to solve: Simplifying -8 + 3z = 0 Solving -8 + 3z = 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 + 3z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3z = 0 + 8 3z = 0 + 8 Combine like terms: 0 + 8 = 8 3z = 8 Divide each side by '3'. z = 2.666666667 Simplifying z = 2.666666667Subproblem 2
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 = 2Solution
z = {2.666666667, 2}
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