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Simplifying 9a + 33ab + -76b + 65c + 17a + 51ab + -80b + 13c = 0 Reorder the terms: 9a + 17a + 33ab + 51ab + -76b + -80b + 65c + 13c = 0 Combine like terms: 9a + 17a = 26a 26a + 33ab + 51ab + -76b + -80b + 65c + 13c = 0 Combine like terms: 33ab + 51ab = 84ab 26a + 84ab + -76b + -80b + 65c + 13c = 0 Combine like terms: -76b + -80b = -156b 26a + 84ab + -156b + 65c + 13c = 0 Combine like terms: 65c + 13c = 78c 26a + 84ab + -156b + 78c = 0 Solving 26a + 84ab + -156b + 78c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '156b' to each side of the equation. 26a + 84ab + -156b + 156b + 78c = 0 + 156b Combine like terms: -156b + 156b = 0 26a + 84ab + 0 + 78c = 0 + 156b 26a + 84ab + 78c = 0 + 156b Remove the zero: 26a + 84ab + 78c = 156b Add '-78c' to each side of the equation. 26a + 84ab + 78c + -78c = 156b + -78c Combine like terms: 78c + -78c = 0 26a + 84ab + 0 = 156b + -78c 26a + 84ab = 156b + -78c Reorder the terms: 26a + 84ab + -156b + 78c = 156b + -156b + -78c + 78c Combine like terms: 156b + -156b = 0 26a + 84ab + -156b + 78c = 0 + -78c + 78c 26a + 84ab + -156b + 78c = -78c + 78c Combine like terms: -78c + 78c = 0 26a + 84ab + -156b + 78c = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13a + 42ab + -78b + 39c) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13a + 42ab + -78b + 39c)' equal to zero and attempt to solve: Simplifying 13a + 42ab + -78b + 39c = 0 Solving 13a + 42ab + -78b + 39c = 0 Move all terms containing a to the left, all other terms to the right. Add '78b' to each side of the equation. 13a + 42ab + -78b + 78b + 39c = 0 + 78b Combine like terms: -78b + 78b = 0 13a + 42ab + 0 + 39c = 0 + 78b 13a + 42ab + 39c = 0 + 78b Remove the zero: 13a + 42ab + 39c = 78b Add '-39c' to each side of the equation. 13a + 42ab + 39c + -39c = 78b + -39c Combine like terms: 39c + -39c = 0 13a + 42ab + 0 = 78b + -39c 13a + 42ab = 78b + -39c 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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