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Simplifying 12a(2b + 7) + (3a + -1) * 15b + -1(74a + 9ab) = 0 Reorder the terms: 12a(7 + 2b) + (3a + -1) * 15b + -1(74a + 9ab) = 0 (7 * 12a + 2b * 12a) + (3a + -1) * 15b + -1(74a + 9ab) = 0 (84a + 24ab) + (3a + -1) * 15b + -1(74a + 9ab) = 0 Reorder the terms: 84a + 24ab + (-1 + 3a) * 15b + -1(74a + 9ab) = 0 Reorder the terms for easier multiplication: 84a + 24ab + 15b(-1 + 3a) + -1(74a + 9ab) = 0 84a + 24ab + (-1 * 15b + 3a * 15b) + -1(74a + 9ab) = 0 Reorder the terms: 84a + 24ab + (45ab + -15b) + -1(74a + 9ab) = 0 84a + 24ab + (45ab + -15b) + -1(74a + 9ab) = 0 84a + 24ab + 45ab + -15b + (74a * -1 + 9ab * -1) = 0 84a + 24ab + 45ab + -15b + (-74a + -9ab) = 0 Reorder the terms: 84a + -74a + 24ab + 45ab + -9ab + -15b = 0 Combine like terms: 84a + -74a = 10a 10a + 24ab + 45ab + -9ab + -15b = 0 Combine like terms: 24ab + 45ab = 69ab 10a + 69ab + -9ab + -15b = 0 Combine like terms: 69ab + -9ab = 60ab 10a + 60ab + -15b = 0 Solving 10a + 60ab + -15b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15b' to each side of the equation. 10a + 60ab + -15b + 15b = 0 + 15b Combine like terms: -15b + 15b = 0 10a + 60ab + 0 = 0 + 15b 10a + 60ab = 0 + 15b Remove the zero: 10a + 60ab = 15b Combine like terms: 15b + -15b = 0 10a + 60ab + -15b = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2a + 12ab + -3b) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2a + 12ab + -3b)' equal to zero and attempt to solve: Simplifying 2a + 12ab + -3b = 0 Solving 2a + 12ab + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 2a + 12ab + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 2a + 12ab + 0 = 0 + 3b 2a + 12ab = 0 + 3b Remove the zero: 2a + 12ab = 3b 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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