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Simplifying (1 + z)(3z + -8) = 0 Reorder the terms: (1 + z)(-8 + 3z) = 0 Multiply (1 + z) * (-8 + 3z) (1(-8 + 3z) + z(-8 + 3z)) = 0 ((-8 * 1 + 3z * 1) + z(-8 + 3z)) = 0 ((-8 + 3z) + z(-8 + 3z)) = 0 (-8 + 3z + (-8 * z + 3z * z)) = 0 (-8 + 3z + (-8z + 3z2)) = 0 Combine like terms: 3z + -8z = -5z (-8 + -5z + 3z2) = 0 Solving -8 + -5z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-1 + -1z)(8 + -3z) = 0Subproblem 1
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 = -1Subproblem 2
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 = 2.666666667Solution
z = {-1, 2.666666667}
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