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Simplifying (8z + -7)(9z + 6) + (8z + -7)(4z + 3) = 0 Reorder the terms: (-7 + 8z)(9z + 6) + (8z + -7)(4z + 3) = 0 Reorder the terms: (-7 + 8z)(6 + 9z) + (8z + -7)(4z + 3) = 0 Multiply (-7 + 8z) * (6 + 9z) (-7(6 + 9z) + 8z * (6 + 9z)) + (8z + -7)(4z + 3) = 0 ((6 * -7 + 9z * -7) + 8z * (6 + 9z)) + (8z + -7)(4z + 3) = 0 ((-42 + -63z) + 8z * (6 + 9z)) + (8z + -7)(4z + 3) = 0 (-42 + -63z + (6 * 8z + 9z * 8z)) + (8z + -7)(4z + 3) = 0 (-42 + -63z + (48z + 72z2)) + (8z + -7)(4z + 3) = 0 Combine like terms: -63z + 48z = -15z (-42 + -15z + 72z2) + (8z + -7)(4z + 3) = 0 Reorder the terms: -42 + -15z + 72z2 + (-7 + 8z)(4z + 3) = 0 Reorder the terms: -42 + -15z + 72z2 + (-7 + 8z)(3 + 4z) = 0 Multiply (-7 + 8z) * (3 + 4z) -42 + -15z + 72z2 + (-7(3 + 4z) + 8z * (3 + 4z)) = 0 -42 + -15z + 72z2 + ((3 * -7 + 4z * -7) + 8z * (3 + 4z)) = 0 -42 + -15z + 72z2 + ((-21 + -28z) + 8z * (3 + 4z)) = 0 -42 + -15z + 72z2 + (-21 + -28z + (3 * 8z + 4z * 8z)) = 0 -42 + -15z + 72z2 + (-21 + -28z + (24z + 32z2)) = 0 Combine like terms: -28z + 24z = -4z -42 + -15z + 72z2 + (-21 + -4z + 32z2) = 0 Reorder the terms: -42 + -21 + -15z + -4z + 72z2 + 32z2 = 0 Combine like terms: -42 + -21 = -63 -63 + -15z + -4z + 72z2 + 32z2 = 0 Combine like terms: -15z + -4z = -19z -63 + -19z + 72z2 + 32z2 = 0 Combine like terms: 72z2 + 32z2 = 104z2 -63 + -19z + 104z2 = 0 Solving -63 + -19z + 104z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -13z)(7 + -8z) = 0Subproblem 1
Set the factor '(-9 + -13z)' equal to zero and attempt to solve: Simplifying -9 + -13z = 0 Solving -9 + -13z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -13z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -13z = 0 + 9 -13z = 0 + 9 Combine like terms: 0 + 9 = 9 -13z = 9 Divide each side by '-13'. z = -0.6923076923 Simplifying z = -0.6923076923Subproblem 2
Set the factor '(7 + -8z)' equal to zero and attempt to solve: Simplifying 7 + -8z = 0 Solving 7 + -8z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -8z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8z = 0 + -7 -8z = 0 + -7 Combine like terms: 0 + -7 = -7 -8z = -7 Divide each side by '-8'. z = 0.875 Simplifying z = 0.875Solution
z = {-0.6923076923, 0.875}
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