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Simplifying (8 + z)(5z + -1) = 0 Reorder the terms: (8 + z)(-1 + 5z) = 0 Multiply (8 + z) * (-1 + 5z) (8(-1 + 5z) + z(-1 + 5z)) = 0 ((-1 * 8 + 5z * 8) + z(-1 + 5z)) = 0 ((-8 + 40z) + z(-1 + 5z)) = 0 (-8 + 40z + (-1 * z + 5z * z)) = 0 (-8 + 40z + (-1z + 5z2)) = 0 Combine like terms: 40z + -1z = 39z (-8 + 39z + 5z2) = 0 Solving -8 + 39z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + -1z)(1 + -5z) = 0Subproblem 1
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 = -8Subproblem 2
Set the factor '(1 + -5z)' equal to zero and attempt to solve: Simplifying 1 + -5z = 0 Solving 1 + -5z = 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 + -5z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5z = 0 + -1 -5z = 0 + -1 Combine like terms: 0 + -1 = -1 -5z = -1 Divide each side by '-5'. z = 0.2 Simplifying z = 0.2Solution
z = {-8, 0.2}
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