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Simplifying (2b + -3)(3b + -8) = 0 Reorder the terms: (-3 + 2b)(3b + -8) = 0 Reorder the terms: (-3 + 2b)(-8 + 3b) = 0 Multiply (-3 + 2b) * (-8 + 3b) (-3(-8 + 3b) + 2b * (-8 + 3b)) = 0 ((-8 * -3 + 3b * -3) + 2b * (-8 + 3b)) = 0 ((24 + -9b) + 2b * (-8 + 3b)) = 0 (24 + -9b + (-8 * 2b + 3b * 2b)) = 0 (24 + -9b + (-16b + 6b2)) = 0 Combine like terms: -9b + -16b = -25b (24 + -25b + 6b2) = 0 Solving 24 + -25b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (3 + -2b)(8 + -3b) = 0Subproblem 1
Set the factor '(3 + -2b)' equal to zero and attempt to solve: Simplifying 3 + -2b = 0 Solving 3 + -2b = 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 + -2b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2b = 0 + -3 -2b = 0 + -3 Combine like terms: 0 + -3 = -3 -2b = -3 Divide each side by '-2'. b = 1.5 Simplifying b = 1.5Subproblem 2
Set the factor '(8 + -3b)' equal to zero and attempt to solve: Simplifying 8 + -3b = 0 Solving 8 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3b = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3b = 0 + -8 -3b = 0 + -8 Combine like terms: 0 + -8 = -8 -3b = -8 Divide each side by '-3'. b = 2.666666667 Simplifying b = 2.666666667Solution
b = {1.5, 2.666666667}
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