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Simplifying (4z + -1)(6z + -5) = 0 Reorder the terms: (-1 + 4z)(6z + -5) = 0 Reorder the terms: (-1 + 4z)(-5 + 6z) = 0 Multiply (-1 + 4z) * (-5 + 6z) (-1(-5 + 6z) + 4z * (-5 + 6z)) = 0 ((-5 * -1 + 6z * -1) + 4z * (-5 + 6z)) = 0 ((5 + -6z) + 4z * (-5 + 6z)) = 0 (5 + -6z + (-5 * 4z + 6z * 4z)) = 0 (5 + -6z + (-20z + 24z2)) = 0 Combine like terms: -6z + -20z = -26z (5 + -26z + 24z2) = 0 Solving 5 + -26z + 24z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -4z)(5 + -6z) = 0Subproblem 1
Set the factor '(1 + -4z)' equal to zero and attempt to solve: Simplifying 1 + -4z = 0 Solving 1 + -4z = 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 + -4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4z = 0 + -1 -4z = 0 + -1 Combine like terms: 0 + -1 = -1 -4z = -1 Divide each side by '-4'. z = 0.25 Simplifying z = 0.25Subproblem 2
Set the factor '(5 + -6z)' equal to zero and attempt to solve: Simplifying 5 + -6z = 0 Solving 5 + -6z = 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 + -6z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6z = 0 + -5 -6z = 0 + -5 Combine like terms: 0 + -5 = -5 -6z = -5 Divide each side by '-6'. z = 0.8333333333 Simplifying z = 0.8333333333Solution
z = {0.25, 0.8333333333}
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