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Simplifying 5b(a + 5) + -1a(5 + -1b) + 3(a + b + -2) = 0 Reorder the terms: 5b(5 + a) + -1a(5 + -1b) + 3(a + b + -2) = 0 (5 * 5b + a * 5b) + -1a(5 + -1b) + 3(a + b + -2) = 0 Reorder the terms: (5ab + 25b) + -1a(5 + -1b) + 3(a + b + -2) = 0 (5ab + 25b) + -1a(5 + -1b) + 3(a + b + -2) = 0 5ab + 25b + (5 * -1a + -1b * -1a) + 3(a + b + -2) = 0 5ab + 25b + (-5a + 1ab) + 3(a + b + -2) = 0 Reorder the terms: 5ab + 25b + -5a + 1ab + 3(-2 + a + b) = 0 5ab + 25b + -5a + 1ab + (-2 * 3 + a * 3 + b * 3) = 0 5ab + 25b + -5a + 1ab + (-6 + 3a + 3b) = 0 Reorder the terms: -6 + -5a + 3a + 5ab + 1ab + 25b + 3b = 0 Combine like terms: -5a + 3a = -2a -6 + -2a + 5ab + 1ab + 25b + 3b = 0 Combine like terms: 5ab + 1ab = 6ab -6 + -2a + 6ab + 25b + 3b = 0 Combine like terms: 25b + 3b = 28b -6 + -2a + 6ab + 28b = 0 Solving -6 + -2a + 6ab + 28b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + -2a + 6ab + 6 + 28b = 0 + 6 Reorder the terms: -6 + 6 + -2a + 6ab + 28b = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2a + 6ab + 28b = 0 + 6 -2a + 6ab + 28b = 0 + 6 Combine like terms: 0 + 6 = 6 -2a + 6ab + 28b = 6 Add '-28b' to each side of the equation. -2a + 6ab + 28b + -28b = 6 + -28b Combine like terms: 28b + -28b = 0 -2a + 6ab + 0 = 6 + -28b -2a + 6ab = 6 + -28b Reorder the terms: -6 + -2a + 6ab + 28b = 6 + -28b + -6 + 28b Reorder the terms: -6 + -2a + 6ab + 28b = 6 + -6 + -28b + 28b Combine like terms: 6 + -6 = 0 -6 + -2a + 6ab + 28b = 0 + -28b + 28b -6 + -2a + 6ab + 28b = -28b + 28b Combine like terms: -28b + 28b = 0 -6 + -2a + 6ab + 28b = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -1a + 3ab + 14b) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1a + 3ab + 14b)' equal to zero and attempt to solve: Simplifying -3 + -1a + 3ab + 14b = 0 Solving -3 + -1a + 3ab + 14b = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -1a + 3ab + 3 + 14b = 0 + 3 Reorder the terms: -3 + 3 + -1a + 3ab + 14b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a + 3ab + 14b = 0 + 3 -1a + 3ab + 14b = 0 + 3 Combine like terms: 0 + 3 = 3 -1a + 3ab + 14b = 3 Add '-14b' to each side of the equation. -1a + 3ab + 14b + -14b = 3 + -14b Combine like terms: 14b + -14b = 0 -1a + 3ab + 0 = 3 + -14b -1a + 3ab = 3 + -14b 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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