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Simplifying (2r + 1)(a + -2) + 5(a + -2) = 0 Reorder the terms: (1 + 2r)(a + -2) + 5(a + -2) = 0 Reorder the terms: (1 + 2r)(-2 + a) + 5(a + -2) = 0 Multiply (1 + 2r) * (-2 + a) (1(-2 + a) + 2r * (-2 + a)) + 5(a + -2) = 0 ((-2 * 1 + a * 1) + 2r * (-2 + a)) + 5(a + -2) = 0 ((-2 + 1a) + 2r * (-2 + a)) + 5(a + -2) = 0 (-2 + 1a + (-2 * 2r + a * 2r)) + 5(a + -2) = 0 Reorder the terms: (-2 + 1a + (2ar + -4r)) + 5(a + -2) = 0 (-2 + 1a + (2ar + -4r)) + 5(a + -2) = 0 (-2 + 1a + 2ar + -4r) + 5(a + -2) = 0 Reorder the terms: -2 + 1a + 2ar + -4r + 5(-2 + a) = 0 -2 + 1a + 2ar + -4r + (-2 * 5 + a * 5) = 0 -2 + 1a + 2ar + -4r + (-10 + 5a) = 0 Reorder the terms: -2 + -10 + 1a + 5a + 2ar + -4r = 0 Combine like terms: -2 + -10 = -12 -12 + 1a + 5a + 2ar + -4r = 0 Combine like terms: 1a + 5a = 6a -12 + 6a + 2ar + -4r = 0 Solving -12 + 6a + 2ar + -4r = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 6a + 2ar + 12 + -4r = 0 + 12 Reorder the terms: -12 + 12 + 6a + 2ar + -4r = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 6a + 2ar + -4r = 0 + 12 6a + 2ar + -4r = 0 + 12 Combine like terms: 0 + 12 = 12 6a + 2ar + -4r = 12 Add '4r' to each side of the equation. 6a + 2ar + -4r + 4r = 12 + 4r Combine like terms: -4r + 4r = 0 6a + 2ar + 0 = 12 + 4r 6a + 2ar = 12 + 4r Reorder the terms: -12 + 6a + 2ar + -4r = 12 + 4r + -12 + -4r Reorder the terms: -12 + 6a + 2ar + -4r = 12 + -12 + 4r + -4r Combine like terms: 12 + -12 = 0 -12 + 6a + 2ar + -4r = 0 + 4r + -4r -12 + 6a + 2ar + -4r = 4r + -4r Combine like terms: 4r + -4r = 0 -12 + 6a + 2ar + -4r = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 3a + ar + -2r) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 3a + ar + -2r)' equal to zero and attempt to solve: Simplifying -6 + 3a + ar + -2r = 0 Solving -6 + 3a + ar + -2r = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 3a + ar + 6 + -2r = 0 + 6 Reorder the terms: -6 + 6 + 3a + ar + -2r = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3a + ar + -2r = 0 + 6 3a + ar + -2r = 0 + 6 Combine like terms: 0 + 6 = 6 3a + ar + -2r = 6 Add '2r' to each side of the equation. 3a + ar + -2r + 2r = 6 + 2r Combine like terms: -2r + 2r = 0 3a + ar + 0 = 6 + 2r 3a + ar = 6 + 2r 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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