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Simplifying 2z(4z + -5) + -1(6z + 7)(6u + 6) = 0 Reorder the terms: 2z(-5 + 4z) + -1(6z + 7)(6u + 6) = 0 (-5 * 2z + 4z * 2z) + -1(6z + 7)(6u + 6) = 0 (-10z + 8z2) + -1(6z + 7)(6u + 6) = 0 Reorder the terms: -10z + 8z2 + -1(7 + 6z)(6u + 6) = 0 Reorder the terms: -10z + 8z2 + -1(7 + 6z)(6 + 6u) = 0 Multiply (7 + 6z) * (6 + 6u) -10z + 8z2 + -1(7(6 + 6u) + 6z * (6 + 6u)) = 0 -10z + 8z2 + -1((6 * 7 + 6u * 7) + 6z * (6 + 6u)) = 0 -10z + 8z2 + -1((42 + 42u) + 6z * (6 + 6u)) = 0 -10z + 8z2 + -1(42 + 42u + (6 * 6z + 6u * 6z)) = 0 Reorder the terms: -10z + 8z2 + -1(42 + 42u + (36uz + 36z)) = 0 -10z + 8z2 + -1(42 + 42u + (36uz + 36z)) = 0 -10z + 8z2 + -1(42 + 42u + 36uz + 36z) = 0 -10z + 8z2 + (42 * -1 + 42u * -1 + 36uz * -1 + 36z * -1) = 0 -10z + 8z2 + (-42 + -42u + -36uz + -36z) = 0 Reorder the terms: -42 + -42u + -36uz + -10z + -36z + 8z2 = 0 Combine like terms: -10z + -36z = -46z -42 + -42u + -36uz + -46z + 8z2 = 0 Solving -42 + -42u + -36uz + -46z + 8z2 = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '42' to each side of the equation. -42 + -42u + -36uz + -46z + 42 + 8z2 = 0 + 42 Reorder the terms: -42 + 42 + -42u + -36uz + -46z + 8z2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -42u + -36uz + -46z + 8z2 = 0 + 42 -42u + -36uz + -46z + 8z2 = 0 + 42 Combine like terms: 0 + 42 = 42 -42u + -36uz + -46z + 8z2 = 42 Add '46z' to each side of the equation. -42u + -36uz + -46z + 46z + 8z2 = 42 + 46z Combine like terms: -46z + 46z = 0 -42u + -36uz + 0 + 8z2 = 42 + 46z -42u + -36uz + 8z2 = 42 + 46z Add '-8z2' to each side of the equation. -42u + -36uz + 8z2 + -8z2 = 42 + 46z + -8z2 Combine like terms: 8z2 + -8z2 = 0 -42u + -36uz + 0 = 42 + 46z + -8z2 -42u + -36uz = 42 + 46z + -8z2 Reorder the terms: -42 + -42u + -36uz + -46z + 8z2 = 42 + 46z + -8z2 + -42 + -46z + 8z2 Reorder the terms: -42 + -42u + -36uz + -46z + 8z2 = 42 + -42 + 46z + -46z + -8z2 + 8z2 Combine like terms: 42 + -42 = 0 -42 + -42u + -36uz + -46z + 8z2 = 0 + 46z + -46z + -8z2 + 8z2 -42 + -42u + -36uz + -46z + 8z2 = 46z + -46z + -8z2 + 8z2 Combine like terms: 46z + -46z = 0 -42 + -42u + -36uz + -46z + 8z2 = 0 + -8z2 + 8z2 -42 + -42u + -36uz + -46z + 8z2 = -8z2 + 8z2 Combine like terms: -8z2 + 8z2 = 0 -42 + -42u + -36uz + -46z + 8z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -21u + -18uz + -23z + 4z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -21u + -18uz + -23z + 4z2)' equal to zero and attempt to solve: Simplifying -21 + -21u + -18uz + -23z + 4z2 = 0 Solving -21 + -21u + -18uz + -23z + 4z2 = 0 Move all terms containing u to the left, all other terms to the right. Add '21' to each side of the equation. -21 + -21u + -18uz + -23z + 21 + 4z2 = 0 + 21 Reorder the terms: -21 + 21 + -21u + -18uz + -23z + 4z2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -21u + -18uz + -23z + 4z2 = 0 + 21 -21u + -18uz + -23z + 4z2 = 0 + 21 Combine like terms: 0 + 21 = 21 -21u + -18uz + -23z + 4z2 = 21 Add '23z' to each side of the equation. -21u + -18uz + -23z + 23z + 4z2 = 21 + 23z Combine like terms: -23z + 23z = 0 -21u + -18uz + 0 + 4z2 = 21 + 23z -21u + -18uz + 4z2 = 21 + 23z Add '-4z2' to each side of the equation. -21u + -18uz + 4z2 + -4z2 = 21 + 23z + -4z2 Combine like terms: 4z2 + -4z2 = 0 -21u + -18uz + 0 = 21 + 23z + -4z2 -21u + -18uz = 21 + 23z + -4z2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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