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Simplifying (2b + -8)(3b + -7) = 0 Reorder the terms: (-8 + 2b)(3b + -7) = 0 Reorder the terms: (-8 + 2b)(-7 + 3b) = 0 Multiply (-8 + 2b) * (-7 + 3b) (-8(-7 + 3b) + 2b * (-7 + 3b)) = 0 ((-7 * -8 + 3b * -8) + 2b * (-7 + 3b)) = 0 ((56 + -24b) + 2b * (-7 + 3b)) = 0 (56 + -24b + (-7 * 2b + 3b * 2b)) = 0 (56 + -24b + (-14b + 6b2)) = 0 Combine like terms: -24b + -14b = -38b (56 + -38b + 6b2) = 0 Solving 56 + -38b + 6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(28 + -19b + 3b2) = 0 Factor a trinomial. 2((7 + -3b)(4 + -1b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -3b)' equal to zero and attempt to solve: Simplifying 7 + -3b = 0 Solving 7 + -3b = 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 + -3b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3b = 0 + -7 -3b = 0 + -7 Combine like terms: 0 + -7 = -7 -3b = -7 Divide each side by '-3'. b = 2.333333333 Simplifying b = 2.333333333Subproblem 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 = {2.333333333, 4}
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