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Simplifying (2b + -7)(b + -4) = 0 Reorder the terms: (-7 + 2b)(b + -4) = 0 Reorder the terms: (-7 + 2b)(-4 + b) = 0 Multiply (-7 + 2b) * (-4 + b) (-7(-4 + b) + 2b * (-4 + b)) = 0 ((-4 * -7 + b * -7) + 2b * (-4 + b)) = 0 ((28 + -7b) + 2b * (-4 + b)) = 0 (28 + -7b + (-4 * 2b + b * 2b)) = 0 (28 + -7b + (-8b + 2b2)) = 0 Combine like terms: -7b + -8b = -15b (28 + -15b + 2b2) = 0 Solving 28 + -15b + 2b2 = 0 Solving for variable 'b'. Factor a trinomial. (7 + -2b)(4 + -1b) = 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 '(4 + -1b)' equal to zero and attempt to solve: Simplifying 4 + -1b = 0 Solving 4 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1b = 0 + -4 -1b = 0 + -4 Combine like terms: 0 + -4 = -4 -1b = -4 Divide each side by '-1'. b = 4 Simplifying b = 4Solution
b = {3.5, 4}
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