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Simplifying (10b + 2)(12a + 9) = 0 Reorder the terms: (2 + 10b)(12a + 9) = 0 Reorder the terms: (2 + 10b)(9 + 12a) = 0 Multiply (2 + 10b) * (9 + 12a) (2(9 + 12a) + 10b * (9 + 12a)) = 0 ((9 * 2 + 12a * 2) + 10b * (9 + 12a)) = 0 ((18 + 24a) + 10b * (9 + 12a)) = 0 (18 + 24a + (9 * 10b + 12a * 10b)) = 0 Reorder the terms: (18 + 24a + (120ab + 90b)) = 0 (18 + 24a + (120ab + 90b)) = 0 (18 + 24a + 120ab + 90b) = 0 Solving 18 + 24a + 120ab + 90b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + 24a + 120ab + -18 + 90b = 0 + -18 Reorder the terms: 18 + -18 + 24a + 120ab + 90b = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 24a + 120ab + 90b = 0 + -18 24a + 120ab + 90b = 0 + -18 Combine like terms: 0 + -18 = -18 24a + 120ab + 90b = -18 Add '-90b' to each side of the equation. 24a + 120ab + 90b + -90b = -18 + -90b Combine like terms: 90b + -90b = 0 24a + 120ab + 0 = -18 + -90b 24a + 120ab = -18 + -90b Reorder the terms: 18 + 24a + 120ab + 90b = -18 + -90b + 18 + 90b Reorder the terms: 18 + 24a + 120ab + 90b = -18 + 18 + -90b + 90b Combine like terms: -18 + 18 = 0 18 + 24a + 120ab + 90b = 0 + -90b + 90b 18 + 24a + 120ab + 90b = -90b + 90b Combine like terms: -90b + 90b = 0 18 + 24a + 120ab + 90b = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(3 + 4a + 20ab + 15b) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + 4a + 20ab + 15b)' equal to zero and attempt to solve: Simplifying 3 + 4a + 20ab + 15b = 0 Solving 3 + 4a + 20ab + 15b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 4a + 20ab + -3 + 15b = 0 + -3 Reorder the terms: 3 + -3 + 4a + 20ab + 15b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4a + 20ab + 15b = 0 + -3 4a + 20ab + 15b = 0 + -3 Combine like terms: 0 + -3 = -3 4a + 20ab + 15b = -3 Add '-15b' to each side of the equation. 4a + 20ab + 15b + -15b = -3 + -15b Combine like terms: 15b + -15b = 0 4a + 20ab + 0 = -3 + -15b 4a + 20ab = -3 + -15b 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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