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Simplifying (2b + 7)(8b + -3) = 0 Reorder the terms: (7 + 2b)(8b + -3) = 0 Reorder the terms: (7 + 2b)(-3 + 8b) = 0 Multiply (7 + 2b) * (-3 + 8b) (7(-3 + 8b) + 2b * (-3 + 8b)) = 0 ((-3 * 7 + 8b * 7) + 2b * (-3 + 8b)) = 0 ((-21 + 56b) + 2b * (-3 + 8b)) = 0 (-21 + 56b + (-3 * 2b + 8b * 2b)) = 0 (-21 + 56b + (-6b + 16b2)) = 0 Combine like terms: 56b + -6b = 50b (-21 + 50b + 16b2) = 0 Solving -21 + 50b + 16b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + -2b)(3 + -8b) = 0Subproblem 1
Set the factor '(-7 + -2b)' equal to zero and attempt to solve: Simplifying -7 + -2b = 0 Solving -7 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2b = 0 + 7 -2b = 0 + 7 Combine like terms: 0 + 7 = 7 -2b = 7 Divide each side by '-2'. b = -3.5 Simplifying b = -3.5Subproblem 2
Set the factor '(3 + -8b)' equal to zero and attempt to solve: Simplifying 3 + -8b = 0 Solving 3 + -8b = 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 + -8b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8b = 0 + -3 -8b = 0 + -3 Combine like terms: 0 + -3 = -3 -8b = -3 Divide each side by '-8'. b = 0.375 Simplifying b = 0.375Solution
b = {-3.5, 0.375}
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