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Simplifying (5z + -1)(8z + -5) = 0 Reorder the terms: (-1 + 5z)(8z + -5) = 0 Reorder the terms: (-1 + 5z)(-5 + 8z) = 0 Multiply (-1 + 5z) * (-5 + 8z) (-1(-5 + 8z) + 5z * (-5 + 8z)) = 0 ((-5 * -1 + 8z * -1) + 5z * (-5 + 8z)) = 0 ((5 + -8z) + 5z * (-5 + 8z)) = 0 (5 + -8z + (-5 * 5z + 8z * 5z)) = 0 (5 + -8z + (-25z + 40z2)) = 0 Combine like terms: -8z + -25z = -33z (5 + -33z + 40z2) = 0 Solving 5 + -33z + 40z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -5z)(5 + -8z) = 0Subproblem 1
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 = 0.2Subproblem 2
Set the factor '(5 + -8z)' equal to zero and attempt to solve: Simplifying 5 + -8z = 0 Solving 5 + -8z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -8z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8z = 0 + -5 -8z = 0 + -5 Combine like terms: 0 + -5 = -5 -8z = -5 Divide each side by '-8'. z = 0.625 Simplifying z = 0.625Solution
z = {0.2, 0.625}
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