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Simplifying (1 + -1z)(3z + -8) = 0 Reorder the terms: (1 + -1z)(-8 + 3z) = 0 Multiply (1 + -1z) * (-8 + 3z) (1(-8 + 3z) + -1z * (-8 + 3z)) = 0 ((-8 * 1 + 3z * 1) + -1z * (-8 + 3z)) = 0 ((-8 + 3z) + -1z * (-8 + 3z)) = 0 (-8 + 3z + (-8 * -1z + 3z * -1z)) = 0 (-8 + 3z + (8z + -3z2)) = 0 Combine like terms: 3z + 8z = 11z (-8 + 11z + -3z2) = 0 Solving -8 + 11z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + 3z)(1 + -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 '(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 = {2.666666667, 1}
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