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Simplifying (4b + -7)(b + -2) = 0 Reorder the terms: (-7 + 4b)(b + -2) = 0 Reorder the terms: (-7 + 4b)(-2 + b) = 0 Multiply (-7 + 4b) * (-2 + b) (-7(-2 + b) + 4b * (-2 + b)) = 0 ((-2 * -7 + b * -7) + 4b * (-2 + b)) = 0 ((14 + -7b) + 4b * (-2 + b)) = 0 (14 + -7b + (-2 * 4b + b * 4b)) = 0 (14 + -7b + (-8b + 4b2)) = 0 Combine like terms: -7b + -8b = -15b (14 + -15b + 4b2) = 0 Solving 14 + -15b + 4b2 = 0 Solving for variable 'b'. Factor a trinomial. (7 + -4b)(2 + -1b) = 0Subproblem 1
Set the factor '(7 + -4b)' equal to zero and attempt to solve: Simplifying 7 + -4b = 0 Solving 7 + -4b = 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 + -4b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4b = 0 + -7 -4b = 0 + -7 Combine like terms: 0 + -7 = -7 -4b = -7 Divide each side by '-4'. b = 1.75 Simplifying b = 1.75Subproblem 2
Set the factor '(2 + -1b)' equal to zero and attempt to solve: Simplifying 2 + -1b = 0 Solving 2 + -1b = 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 + -1b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1b = 0 + -2 -1b = 0 + -2 Combine like terms: 0 + -2 = -2 -1b = -2 Divide each side by '-1'. b = 2 Simplifying b = 2Solution
b = {1.75, 2}
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