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Simplifying (4b + -2)(5b + 1) + -1(1 + 5b)(2b + -4) = 0 Reorder the terms: (-2 + 4b)(5b + 1) + -1(1 + 5b)(2b + -4) = 0 Reorder the terms: (-2 + 4b)(1 + 5b) + -1(1 + 5b)(2b + -4) = 0 Multiply (-2 + 4b) * (1 + 5b) (-2(1 + 5b) + 4b * (1 + 5b)) + -1(1 + 5b)(2b + -4) = 0 ((1 * -2 + 5b * -2) + 4b * (1 + 5b)) + -1(1 + 5b)(2b + -4) = 0 ((-2 + -10b) + 4b * (1 + 5b)) + -1(1 + 5b)(2b + -4) = 0 (-2 + -10b + (1 * 4b + 5b * 4b)) + -1(1 + 5b)(2b + -4) = 0 (-2 + -10b + (4b + 20b2)) + -1(1 + 5b)(2b + -4) = 0 Combine like terms: -10b + 4b = -6b (-2 + -6b + 20b2) + -1(1 + 5b)(2b + -4) = 0 Reorder the terms: -2 + -6b + 20b2 + -1(1 + 5b)(-4 + 2b) = 0 Multiply (1 + 5b) * (-4 + 2b) -2 + -6b + 20b2 + -1(1(-4 + 2b) + 5b * (-4 + 2b)) = 0 -2 + -6b + 20b2 + -1((-4 * 1 + 2b * 1) + 5b * (-4 + 2b)) = 0 -2 + -6b + 20b2 + -1((-4 + 2b) + 5b * (-4 + 2b)) = 0 -2 + -6b + 20b2 + -1(-4 + 2b + (-4 * 5b + 2b * 5b)) = 0 -2 + -6b + 20b2 + -1(-4 + 2b + (-20b + 10b2)) = 0 Combine like terms: 2b + -20b = -18b -2 + -6b + 20b2 + -1(-4 + -18b + 10b2) = 0 -2 + -6b + 20b2 + (-4 * -1 + -18b * -1 + 10b2 * -1) = 0 -2 + -6b + 20b2 + (4 + 18b + -10b2) = 0 Reorder the terms: -2 + 4 + -6b + 18b + 20b2 + -10b2 = 0 Combine like terms: -2 + 4 = 2 2 + -6b + 18b + 20b2 + -10b2 = 0 Combine like terms: -6b + 18b = 12b 2 + 12b + 20b2 + -10b2 = 0 Combine like terms: 20b2 + -10b2 = 10b2 2 + 12b + 10b2 = 0 Solving 2 + 12b + 10b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 6b + 5b2) = 0 Factor a trinomial. 2((1 + b)(1 + 5b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + b)' equal to zero and attempt to solve: Simplifying 1 + b = 0 Solving 1 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + b = 0 + -1 b = 0 + -1 Combine like terms: 0 + -1 = -1 b = -1 Simplifying b = -1Subproblem 2
Set the factor '(1 + 5b)' equal to zero and attempt to solve: Simplifying 1 + 5b = 0 Solving 1 + 5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5b = 0 + -1 5b = 0 + -1 Combine like terms: 0 + -1 = -1 5b = -1 Divide each side by '5'. b = -0.2 Simplifying b = -0.2Solution
b = {-1, -0.2}
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