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Simplifying (12a2b + 8a + -5a2b + 2ab) + -1(4ab2 + 6ab + -2a + -3ab) = 0 Reorder the terms: (8a + 2ab + 12a2b + -5a2b) + -1(4ab2 + 6ab + -2a + -3ab) = 0 Combine like terms: 12a2b + -5a2b = 7a2b (8a + 2ab + 7a2b) + -1(4ab2 + 6ab + -2a + -3ab) = 0 Remove parenthesis around (8a + 2ab + 7a2b) 8a + 2ab + 7a2b + -1(4ab2 + 6ab + -2a + -3ab) = 0 Reorder the terms: 8a + 2ab + 7a2b + -1(-2a + 6ab + -3ab + 4ab2) = 0 Combine like terms: 6ab + -3ab = 3ab 8a + 2ab + 7a2b + -1(-2a + 3ab + 4ab2) = 0 8a + 2ab + 7a2b + (-2a * -1 + 3ab * -1 + 4ab2 * -1) = 0 8a + 2ab + 7a2b + (2a + -3ab + -4ab2) = 0 Reorder the terms: 8a + 2a + 2ab + -3ab + -4ab2 + 7a2b = 0 Combine like terms: 8a + 2a = 10a 10a + 2ab + -3ab + -4ab2 + 7a2b = 0 Combine like terms: 2ab + -3ab = -1ab 10a + -1ab + -4ab2 + 7a2b = 0 Solving 10a + -1ab + -4ab2 + 7a2b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(10 + -1b + -4b2 + 7ab) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(10 + -1b + -4b2 + 7ab)' equal to zero and attempt to solve: Simplifying 10 + -1b + -4b2 + 7ab = 0 Reorder the terms: 10 + 7ab + -1b + -4b2 = 0 Solving 10 + 7ab + -1b + -4b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + 7ab + -1b + -10 + -4b2 = 0 + -10 Reorder the terms: 10 + -10 + 7ab + -1b + -4b2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 7ab + -1b + -4b2 = 0 + -10 7ab + -1b + -4b2 = 0 + -10 Combine like terms: 0 + -10 = -10 7ab + -1b + -4b2 = -10 Add 'b' to each side of the equation. 7ab + -1b + b + -4b2 = -10 + b Combine like terms: -1b + b = 0 7ab + 0 + -4b2 = -10 + b 7ab + -4b2 = -10 + b Add '4b2' to each side of the equation. 7ab + -4b2 + 4b2 = -10 + b + 4b2 Combine like terms: -4b2 + 4b2 = 0 7ab + 0 = -10 + b + 4b2 7ab = -10 + b + 4b2 Divide each side by '7b'. a = -1.428571429b-1 + 0.1428571429 + 0.5714285714b Simplifying a = -1.428571429b-1 + 0.1428571429 + 0.5714285714b Reorder the terms: a = 0.1428571429 + -1.428571429b-1 + 0.5714285714bSolution
a = {0, 0.1428571429 + -1.428571429b-1 + 0.5714285714b}
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