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Simplifying (-2b + 7)(4b + -3) = 0 Reorder the terms: (7 + -2b)(4b + -3) = 0 Reorder the terms: (7 + -2b)(-3 + 4b) = 0 Multiply (7 + -2b) * (-3 + 4b) (7(-3 + 4b) + -2b * (-3 + 4b)) = 0 ((-3 * 7 + 4b * 7) + -2b * (-3 + 4b)) = 0 ((-21 + 28b) + -2b * (-3 + 4b)) = 0 (-21 + 28b + (-3 * -2b + 4b * -2b)) = 0 (-21 + 28b + (6b + -8b2)) = 0 Combine like terms: 28b + 6b = 34b (-21 + 34b + -8b2) = 0 Solving -21 + 34b + -8b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + 2b)(3 + -4b) = 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 + -4b)' equal to zero and attempt to solve: Simplifying 3 + -4b = 0 Solving 3 + -4b = 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 + -4b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4b = 0 + -3 -4b = 0 + -3 Combine like terms: 0 + -3 = -3 -4b = -3 Divide each side by '-4'. b = 0.75 Simplifying b = 0.75Solution
b = {3.5, 0.75}
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