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Simplifying (4z + -1)(3z + 5) = 0 Reorder the terms: (-1 + 4z)(3z + 5) = 0 Reorder the terms: (-1 + 4z)(5 + 3z) = 0 Multiply (-1 + 4z) * (5 + 3z) (-1(5 + 3z) + 4z * (5 + 3z)) = 0 ((5 * -1 + 3z * -1) + 4z * (5 + 3z)) = 0 ((-5 + -3z) + 4z * (5 + 3z)) = 0 (-5 + -3z + (5 * 4z + 3z * 4z)) = 0 (-5 + -3z + (20z + 12z2)) = 0 Combine like terms: -3z + 20z = 17z (-5 + 17z + 12z2) = 0 Solving -5 + 17z + 12z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + -3z)(1 + -4z) = 0Subproblem 1
Set the factor '(-5 + -3z)' equal to zero and attempt to solve: Simplifying -5 + -3z = 0 Solving -5 + -3z = 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 + -3z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3z = 0 + 5 -3z = 0 + 5 Combine like terms: 0 + 5 = 5 -3z = 5 Divide each side by '-3'. z = -1.666666667 Simplifying z = -1.666666667Subproblem 2
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 = 0.25Solution
z = {-1.666666667, 0.25}
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