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Simplifying 3b2 + -1b + -7 = 4b(2b + 3) + -1 Reorder the terms: -7 + -1b + 3b2 = 4b(2b + 3) + -1 Reorder the terms: -7 + -1b + 3b2 = 4b(3 + 2b) + -1 -7 + -1b + 3b2 = (3 * 4b + 2b * 4b) + -1 -7 + -1b + 3b2 = (12b + 8b2) + -1 Reorder the terms: -7 + -1b + 3b2 = -1 + 12b + 8b2 Solving -7 + -1b + 3b2 = -1 + 12b + 8b2 Solving for variable 'b'. Reorder the terms: -7 + 1 + -1b + -12b + 3b2 + -8b2 = -1 + 12b + 8b2 + 1 + -12b + -8b2 Combine like terms: -7 + 1 = -6 -6 + -1b + -12b + 3b2 + -8b2 = -1 + 12b + 8b2 + 1 + -12b + -8b2 Combine like terms: -1b + -12b = -13b -6 + -13b + 3b2 + -8b2 = -1 + 12b + 8b2 + 1 + -12b + -8b2 Combine like terms: 3b2 + -8b2 = -5b2 -6 + -13b + -5b2 = -1 + 12b + 8b2 + 1 + -12b + -8b2 Reorder the terms: -6 + -13b + -5b2 = -1 + 1 + 12b + -12b + 8b2 + -8b2 Combine like terms: -1 + 1 = 0 -6 + -13b + -5b2 = 0 + 12b + -12b + 8b2 + -8b2 -6 + -13b + -5b2 = 12b + -12b + 8b2 + -8b2 Combine like terms: 12b + -12b = 0 -6 + -13b + -5b2 = 0 + 8b2 + -8b2 -6 + -13b + -5b2 = 8b2 + -8b2 Combine like terms: 8b2 + -8b2 = 0 -6 + -13b + -5b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 13b + 5b2) = 0 Factor a trinomial. -1((2 + b)(3 + 5b)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + b)' equal to zero and attempt to solve: Simplifying 2 + b = 0 Solving 2 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + b = 0 + -2 b = 0 + -2 Combine like terms: 0 + -2 = -2 b = -2 Simplifying b = -2Subproblem 2
Set the factor '(3 + 5b)' equal to zero and attempt to solve: Simplifying 3 + 5b = 0 Solving 3 + 5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5b = 0 + -3 5b = 0 + -3 Combine like terms: 0 + -3 = -3 5b = -3 Divide each side by '5'. b = -0.6 Simplifying b = -0.6Solution
b = {-2, -0.6}
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