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Simplifying (5b + 1)(4b + -3) = 0 Reorder the terms: (1 + 5b)(4b + -3) = 0 Reorder the terms: (1 + 5b)(-3 + 4b) = 0 Multiply (1 + 5b) * (-3 + 4b) (1(-3 + 4b) + 5b * (-3 + 4b)) = 0 ((-3 * 1 + 4b * 1) + 5b * (-3 + 4b)) = 0 ((-3 + 4b) + 5b * (-3 + 4b)) = 0 (-3 + 4b + (-3 * 5b + 4b * 5b)) = 0 (-3 + 4b + (-15b + 20b2)) = 0 Combine like terms: 4b + -15b = -11b (-3 + -11b + 20b2) = 0 Solving -3 + -11b + 20b2 = 0 Solving for variable 'b'. Factor a trinomial. (-1 + -5b)(3 + -4b) = 0Subproblem 1
Set the factor '(-1 + -5b)' equal to zero and attempt to solve: Simplifying -1 + -5b = 0 Solving -1 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -5b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5b = 0 + 1 -5b = 0 + 1 Combine like terms: 0 + 1 = 1 -5b = 1 Divide each side by '-5'. b = -0.2 Simplifying b = -0.2Subproblem 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 = {-0.2, 0.75}
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