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Simplifying (8a + 2b + -4)(3b + -5) = 0 Reorder the terms: (-4 + 8a + 2b)(3b + -5) = 0 Reorder the terms: (-4 + 8a + 2b)(-5 + 3b) = 0 Multiply (-4 + 8a + 2b) * (-5 + 3b) (-4(-5 + 3b) + 8a * (-5 + 3b) + 2b * (-5 + 3b)) = 0 ((-5 * -4 + 3b * -4) + 8a * (-5 + 3b) + 2b * (-5 + 3b)) = 0 ((20 + -12b) + 8a * (-5 + 3b) + 2b * (-5 + 3b)) = 0 (20 + -12b + (-5 * 8a + 3b * 8a) + 2b * (-5 + 3b)) = 0 (20 + -12b + (-40a + 24ab) + 2b * (-5 + 3b)) = 0 (20 + -12b + -40a + 24ab + (-5 * 2b + 3b * 2b)) = 0 (20 + -12b + -40a + 24ab + (-10b + 6b2)) = 0 Reorder the terms: (20 + -40a + 24ab + -12b + -10b + 6b2) = 0 Combine like terms: -12b + -10b = -22b (20 + -40a + 24ab + -22b + 6b2) = 0 Solving 20 + -40a + 24ab + -22b + 6b2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -40a + 24ab + -22b + -20 + 6b2 = 0 + -20 Reorder the terms: 20 + -20 + -40a + 24ab + -22b + 6b2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -40a + 24ab + -22b + 6b2 = 0 + -20 -40a + 24ab + -22b + 6b2 = 0 + -20 Combine like terms: 0 + -20 = -20 -40a + 24ab + -22b + 6b2 = -20 Add '22b' to each side of the equation. -40a + 24ab + -22b + 22b + 6b2 = -20 + 22b Combine like terms: -22b + 22b = 0 -40a + 24ab + 0 + 6b2 = -20 + 22b -40a + 24ab + 6b2 = -20 + 22b Add '-6b2' to each side of the equation. -40a + 24ab + 6b2 + -6b2 = -20 + 22b + -6b2 Combine like terms: 6b2 + -6b2 = 0 -40a + 24ab + 0 = -20 + 22b + -6b2 -40a + 24ab = -20 + 22b + -6b2 Reorder the terms: 20 + -40a + 24ab + -22b + 6b2 = -20 + 22b + -6b2 + 20 + -22b + 6b2 Reorder the terms: 20 + -40a + 24ab + -22b + 6b2 = -20 + 20 + 22b + -22b + -6b2 + 6b2 Combine like terms: -20 + 20 = 0 20 + -40a + 24ab + -22b + 6b2 = 0 + 22b + -22b + -6b2 + 6b2 20 + -40a + 24ab + -22b + 6b2 = 22b + -22b + -6b2 + 6b2 Combine like terms: 22b + -22b = 0 20 + -40a + 24ab + -22b + 6b2 = 0 + -6b2 + 6b2 20 + -40a + 24ab + -22b + 6b2 = -6b2 + 6b2 Combine like terms: -6b2 + 6b2 = 0 20 + -40a + 24ab + -22b + 6b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -20a + 12ab + -11b + 3b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -20a + 12ab + -11b + 3b2)' equal to zero and attempt to solve: Simplifying 10 + -20a + 12ab + -11b + 3b2 = 0 Solving 10 + -20a + 12ab + -11b + 3b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -20a + 12ab + -11b + -10 + 3b2 = 0 + -10 Reorder the terms: 10 + -10 + -20a + 12ab + -11b + 3b2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -20a + 12ab + -11b + 3b2 = 0 + -10 -20a + 12ab + -11b + 3b2 = 0 + -10 Combine like terms: 0 + -10 = -10 -20a + 12ab + -11b + 3b2 = -10 Add '11b' to each side of the equation. -20a + 12ab + -11b + 11b + 3b2 = -10 + 11b Combine like terms: -11b + 11b = 0 -20a + 12ab + 0 + 3b2 = -10 + 11b -20a + 12ab + 3b2 = -10 + 11b Add '-3b2' to each side of the equation. -20a + 12ab + 3b2 + -3b2 = -10 + 11b + -3b2 Combine like terms: 3b2 + -3b2 = 0 -20a + 12ab + 0 = -10 + 11b + -3b2 -20a + 12ab = -10 + 11b + -3b2 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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