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Simplifying (2b + -5)(3b + -7) = 0 Reorder the terms: (-5 + 2b)(3b + -7) = 0 Reorder the terms: (-5 + 2b)(-7 + 3b) = 0 Multiply (-5 + 2b) * (-7 + 3b) (-5(-7 + 3b) + 2b * (-7 + 3b)) = 0 ((-7 * -5 + 3b * -5) + 2b * (-7 + 3b)) = 0 ((35 + -15b) + 2b * (-7 + 3b)) = 0 (35 + -15b + (-7 * 2b + 3b * 2b)) = 0 (35 + -15b + (-14b + 6b2)) = 0 Combine like terms: -15b + -14b = -29b (35 + -29b + 6b2) = 0 Solving 35 + -29b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (7 + -3b)(5 + -2b) = 0Subproblem 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 '(5 + -2b)' equal to zero and attempt to solve: Simplifying 5 + -2b = 0 Solving 5 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2b = 0 + -5 -2b = 0 + -5 Combine like terms: 0 + -5 = -5 -2b = -5 Divide each side by '-2'. b = 2.5 Simplifying b = 2.5Solution
b = {2.333333333, 2.5}
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