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Simplifying (2a + 1)(2b + -1) = 143 Reorder the terms: (1 + 2a)(2b + -1) = 143 Reorder the terms: (1 + 2a)(-1 + 2b) = 143 Multiply (1 + 2a) * (-1 + 2b) (1(-1 + 2b) + 2a * (-1 + 2b)) = 143 ((-1 * 1 + 2b * 1) + 2a * (-1 + 2b)) = 143 ((-1 + 2b) + 2a * (-1 + 2b)) = 143 (-1 + 2b + (-1 * 2a + 2b * 2a)) = 143 (-1 + 2b + (-2a + 4ab)) = 143 Reorder the terms: (-1 + -2a + 4ab + 2b) = 143 (-1 + -2a + 4ab + 2b) = 143 Solving -1 + -2a + 4ab + 2b = 143 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -2a + 4ab + 1 + 2b = 143 + 1 Reorder the terms: -1 + 1 + -2a + 4ab + 2b = 143 + 1 Combine like terms: -1 + 1 = 0 0 + -2a + 4ab + 2b = 143 + 1 -2a + 4ab + 2b = 143 + 1 Combine like terms: 143 + 1 = 144 -2a + 4ab + 2b = 144 Add '-2b' to each side of the equation. -2a + 4ab + 2b + -2b = 144 + -2b Combine like terms: 2b + -2b = 0 -2a + 4ab + 0 = 144 + -2b -2a + 4ab = 144 + -2b Reorder the terms: -144 + -2a + 4ab + 2b = 144 + -2b + -144 + 2b Reorder the terms: -144 + -2a + 4ab + 2b = 144 + -144 + -2b + 2b Combine like terms: 144 + -144 = 0 -144 + -2a + 4ab + 2b = 0 + -2b + 2b -144 + -2a + 4ab + 2b = -2b + 2b Combine like terms: -2b + 2b = 0 -144 + -2a + 4ab + 2b = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + -1a + 2ab + b) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + -1a + 2ab + b)' equal to zero and attempt to solve: Simplifying -72 + -1a + 2ab + b = 0 Solving -72 + -1a + 2ab + b = 0 Move all terms containing a to the left, all other terms to the right. Add '72' to each side of the equation. -72 + -1a + 2ab + 72 + b = 0 + 72 Reorder the terms: -72 + 72 + -1a + 2ab + b = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -1a + 2ab + b = 0 + 72 -1a + 2ab + b = 0 + 72 Combine like terms: 0 + 72 = 72 -1a + 2ab + b = 72 Add '-1b' to each side of the equation. -1a + 2ab + b + -1b = 72 + -1b Combine like terms: b + -1b = 0 -1a + 2ab + 0 = 72 + -1b -1a + 2ab = 72 + -1b 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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