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Simplifying (8z + -5)(2z + 7) + (8z + -5)(6z + 4) = 0 Reorder the terms: (-5 + 8z)(2z + 7) + (8z + -5)(6z + 4) = 0 Reorder the terms: (-5 + 8z)(7 + 2z) + (8z + -5)(6z + 4) = 0 Multiply (-5 + 8z) * (7 + 2z) (-5(7 + 2z) + 8z * (7 + 2z)) + (8z + -5)(6z + 4) = 0 ((7 * -5 + 2z * -5) + 8z * (7 + 2z)) + (8z + -5)(6z + 4) = 0 ((-35 + -10z) + 8z * (7 + 2z)) + (8z + -5)(6z + 4) = 0 (-35 + -10z + (7 * 8z + 2z * 8z)) + (8z + -5)(6z + 4) = 0 (-35 + -10z + (56z + 16z2)) + (8z + -5)(6z + 4) = 0 Combine like terms: -10z + 56z = 46z (-35 + 46z + 16z2) + (8z + -5)(6z + 4) = 0 Reorder the terms: -35 + 46z + 16z2 + (-5 + 8z)(6z + 4) = 0 Reorder the terms: -35 + 46z + 16z2 + (-5 + 8z)(4 + 6z) = 0 Multiply (-5 + 8z) * (4 + 6z) -35 + 46z + 16z2 + (-5(4 + 6z) + 8z * (4 + 6z)) = 0 -35 + 46z + 16z2 + ((4 * -5 + 6z * -5) + 8z * (4 + 6z)) = 0 -35 + 46z + 16z2 + ((-20 + -30z) + 8z * (4 + 6z)) = 0 -35 + 46z + 16z2 + (-20 + -30z + (4 * 8z + 6z * 8z)) = 0 -35 + 46z + 16z2 + (-20 + -30z + (32z + 48z2)) = 0 Combine like terms: -30z + 32z = 2z -35 + 46z + 16z2 + (-20 + 2z + 48z2) = 0 Reorder the terms: -35 + -20 + 46z + 2z + 16z2 + 48z2 = 0 Combine like terms: -35 + -20 = -55 -55 + 46z + 2z + 16z2 + 48z2 = 0 Combine like terms: 46z + 2z = 48z -55 + 48z + 16z2 + 48z2 = 0 Combine like terms: 16z2 + 48z2 = 64z2 -55 + 48z + 64z2 = 0 Solving -55 + 48z + 64z2 = 0 Solving for variable 'z'. Factor a trinomial. (-11 + -8z)(5 + -8z) = 0Subproblem 1
Set the factor '(-11 + -8z)' equal to zero and attempt to solve: Simplifying -11 + -8z = 0 Solving -11 + -8z = 0 Move all terms containing z to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -8z = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -8z = 0 + 11 -8z = 0 + 11 Combine like terms: 0 + 11 = 11 -8z = 11 Divide each side by '-8'. z = -1.375 Simplifying z = -1.375Subproblem 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 = {-1.375, 0.625}
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