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Simplifying (10b + 7)(3b + -9) = 0 Reorder the terms: (7 + 10b)(3b + -9) = 0 Reorder the terms: (7 + 10b)(-9 + 3b) = 0 Multiply (7 + 10b) * (-9 + 3b) (7(-9 + 3b) + 10b * (-9 + 3b)) = 0 ((-9 * 7 + 3b * 7) + 10b * (-9 + 3b)) = 0 ((-63 + 21b) + 10b * (-9 + 3b)) = 0 (-63 + 21b + (-9 * 10b + 3b * 10b)) = 0 (-63 + 21b + (-90b + 30b2)) = 0 Combine like terms: 21b + -90b = -69b (-63 + -69b + 30b2) = 0 Solving -63 + -69b + 30b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + -23b + 10b2) = 0 Factor a trinomial. 3((-7 + -10b)(3 + -1b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -10b)' equal to zero and attempt to solve: Simplifying -7 + -10b = 0 Solving -7 + -10b = 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 + -10b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10b = 0 + 7 -10b = 0 + 7 Combine like terms: 0 + 7 = 7 -10b = 7 Divide each side by '-10'. b = -0.7 Simplifying b = -0.7Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 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 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3Solution
b = {-0.7, 3}
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